Probability & Statistics interview questions

1. A.the continuous distribution of constant density over a finite interval, whose mean is the midpoint of that interval
2. B.the probability of one event given that another has occurred, obtained by dividing the joint probability by the probability of the conditioning event
3. C.the sum or mean of a large number of independent identically distributed variables of finite variance is approximately normally distributed regardless of the parent distribution
4. D.reverses a conditional probability by weighting each hypothesis by its prior and normalising over all hypotheses

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1. A.Exponential distribution
2. B.Conditional probability
3. C.Coefficient of variation
4. D.Normal distribution

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1. A.Conditional probability — events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
2. B.Conditional probability — the sum or mean of a large number of independent identically distributed variables of finite variance is approximately normally distributed regardless of the parent distribution
3. C.Conditional probability — the probability of one event given that another has occurred, obtained by dividing the joint probability by the probability of the conditioning event
4. D.Conditional probability — the ratio of the standard deviation to the mean, a dimensionless measure allowing dispersion to be compared across differently scaled data

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1. A.events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
2. B.the ratio of the standard deviation to the mean, a dimensionless measure allowing dispersion to be compared across differently scaled data
3. C.the distribution of the count of rare independent events in a fixed interval, whose mean and variance are equal
4. D.the memoryless continuous distribution of the waiting time between successive events of a Poisson process

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1. A.Coefficient of variation
2. B.Bayes' theorem
3. C.Central limit theorem
4. D.Mutually exclusive events

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1. A.Mutually exclusive events — the symmetric bell-shaped continuous distribution specified by its mean and variance, in which about ninety-five percent of the mass lies within two standard deviations of the mean
2. B.Mutually exclusive events — events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
3. C.Mutually exclusive events — the continuous distribution of constant density over a finite interval, whose mean is the midpoint of that interval
4. D.Mutually exclusive events — reverses a conditional probability by weighting each hypothesis by its prior and normalising over all hypotheses

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1. A.the ratio of the standard deviation to the mean, a dimensionless measure allowing dispersion to be compared across differently scaled data
2. B.events for which the joint probability factorises into the product of the individual probabilities, so one occurring does not change the other's chance
3. C.the memoryless continuous distribution of the waiting time between successive events of a Poisson process
4. D.reverses a conditional probability by weighting each hypothesis by its prior and normalising over all hypotheses

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1. A.Binomial distribution
2. B.Central limit theorem
3. C.Poisson distribution
4. D.Independent events

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1. A.Independent events — the ratio of the standard deviation to the mean, a dimensionless measure allowing dispersion to be compared across differently scaled data
2. B.Independent events — the symmetric bell-shaped continuous distribution specified by its mean and variance, in which about ninety-five percent of the mass lies within two standard deviations of the mean
3. C.Independent events — events for which the joint probability factorises into the product of the individual probabilities, so one occurring does not change the other's chance
4. D.Independent events — the probability of one event given that another has occurred, obtained by dividing the joint probability by the probability of the conditioning event

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1. A.the ratio of the standard deviation to the mean, a dimensionless measure allowing dispersion to be compared across differently scaled data
2. B.the sum or mean of a large number of independent identically distributed variables of finite variance is approximately normally distributed regardless of the parent distribution
3. C.a dimensionless measure between minus one and one of the strength and direction of the linear association between two variables
4. D.reverses a conditional probability by weighting each hypothesis by its prior and normalising over all hypotheses

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1. A.Poisson distribution
2. B.Mutually exclusive events
3. C.Independent events
4. D.Bayes' theorem

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1. A.Bayes' theorem — events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
2. B.Bayes' theorem — a dimensionless measure between minus one and one of the strength and direction of the linear association between two variables
3. C.Bayes' theorem — reverses a conditional probability by weighting each hypothesis by its prior and normalising over all hypotheses
4. D.Bayes' theorem — the distribution of the number of successes in a fixed number of independent trials each having the same success probability

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1. A.the probability of one event given that another has occurred, obtained by dividing the joint probability by the probability of the conditioning event
2. B.the memoryless continuous distribution of the waiting time between successive events of a Poisson process
3. C.the distribution of the number of successes in a fixed number of independent trials each having the same success probability
4. D.a dimensionless measure between minus one and one of the strength and direction of the linear association between two variables

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1. A.Binomial distribution
2. B.Independent events
3. C.Conditional probability
4. D.Uniform distribution on an interval

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1. A.Binomial distribution — the ratio of the standard deviation to the mean, a dimensionless measure allowing dispersion to be compared across differently scaled data
2. B.Binomial distribution — the memoryless continuous distribution of the waiting time between successive events of a Poisson process
3. C.Binomial distribution — the sum or mean of a large number of independent identically distributed variables of finite variance is approximately normally distributed regardless of the parent distribution
4. D.Binomial distribution — the distribution of the number of successes in a fixed number of independent trials each having the same success probability

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1. A.the distribution of the count of rare independent events in a fixed interval, whose mean and variance are equal
2. B.the probability of one event given that another has occurred, obtained by dividing the joint probability by the probability of the conditioning event
3. C.the ratio of the standard deviation to the mean, a dimensionless measure allowing dispersion to be compared across differently scaled data
4. D.events for which the joint probability factorises into the product of the individual probabilities, so one occurring does not change the other's chance

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1. A.Coefficient of variation
2. B.Poisson distribution
3. C.Mutually exclusive events
4. D.Binomial distribution

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1. A.Poisson distribution — events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
2. B.Poisson distribution — the distribution of the number of successes in a fixed number of independent trials each having the same success probability
3. C.Poisson distribution — the distribution of the count of rare independent events in a fixed interval, whose mean and variance are equal
4. D.Poisson distribution — a dimensionless measure between minus one and one of the strength and direction of the linear association between two variables

Answer + AI explanation with Pro

1. A.the probability of one event given that another has occurred, obtained by dividing the joint probability by the probability of the conditioning event
2. B.events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
3. C.reverses a conditional probability by weighting each hypothesis by its prior and normalising over all hypotheses
4. D.the memoryless continuous distribution of the waiting time between successive events of a Poisson process

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1. A.Bayes' theorem
2. B.Central limit theorem
3. C.Exponential distribution
4. D.Poisson distribution

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1. A.Exponential distribution — events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
2. B.Exponential distribution — the memoryless continuous distribution of the waiting time between successive events of a Poisson process
3. C.Exponential distribution — the ratio of the standard deviation to the mean, a dimensionless measure allowing dispersion to be compared across differently scaled data
4. D.Exponential distribution — reverses a conditional probability by weighting each hypothesis by its prior and normalising over all hypotheses

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1. A.events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
2. B.the continuous distribution of constant density over a finite interval, whose mean is the midpoint of that interval
3. C.the symmetric bell-shaped continuous distribution specified by its mean and variance, in which about ninety-five percent of the mass lies within two standard deviations of the mean
4. D.a dimensionless measure between minus one and one of the strength and direction of the linear association between two variables

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1. A.Uniform distribution on an interval
2. B.Binomial distribution
3. C.Normal distribution
4. D.Poisson distribution

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1. A.Normal distribution — events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
2. B.Normal distribution — reverses a conditional probability by weighting each hypothesis by its prior and normalising over all hypotheses
3. C.Normal distribution — the probability of one event given that another has occurred, obtained by dividing the joint probability by the probability of the conditioning event
4. D.Normal distribution — the symmetric bell-shaped continuous distribution specified by its mean and variance, in which about ninety-five percent of the mass lies within two standard deviations of the mean

Answer + AI explanation with Pro

1. A.events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
2. B.the continuous distribution of constant density over a finite interval, whose mean is the midpoint of that interval
3. C.the memoryless continuous distribution of the waiting time between successive events of a Poisson process
4. D.the probability of one event given that another has occurred, obtained by dividing the joint probability by the probability of the conditioning event

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1. A.Coefficient of variation
2. B.Uniform distribution on an interval
3. C.Conditional probability
4. D.Exponential distribution

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1. A.Uniform distribution on an interval — the distribution of the count of rare independent events in a fixed interval, whose mean and variance are equal
2. B.Uniform distribution on an interval — events that cannot occur together, so their joint probability is zero and the probability of their union is the sum of the individual probabilities
3. C.Uniform distribution on an interval — a dimensionless measure between minus one and one of the strength and direction of the linear association between two variables
4. D.Uniform distribution on an interval — the continuous distribution of constant density over a finite interval, whose mean is the midpoint of that interval

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1. A.the distribution of the number of successes in a fixed number of independent trials each having the same success probability
2. B.the distribution of the count of rare independent events in a fixed interval, whose mean and variance are equal
3. C.the sum or mean of a large number of independent identically distributed variables of finite variance is approximately normally distributed regardless of the parent distribution
4. D.the symmetric bell-shaped continuous distribution specified by its mean and variance, in which about ninety-five percent of the mass lies within two standard deviations of the mean

Answer + AI explanation with Pro

1. A.Binomial distribution
2. B.Conditional probability
3. C.Central limit theorem
4. D.Independent events

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1. A.Central limit theorem — the ratio of the standard deviation to the mean, a dimensionless measure allowing dispersion to be compared across differently scaled data
2. B.Central limit theorem — the sum or mean of a large number of independent identically distributed variables of finite variance is approximately normally distributed regardless of the parent distribution
3. C.Central limit theorem — reverses a conditional probability by weighting each hypothesis by its prior and normalising over all hypotheses
4. D.Central limit theorem — events for which the joint probability factorises into the product of the individual probabilities, so one occurring does not change the other's chance

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