DTSA 5001 CERTIFICATION EXAMINATION
2026 PREMIUM QUESTIONS AND
SOLUTIONS
◉ Expected value of exponential distribution.
Answer: 1/lambda
◉ Law of the Unconscious Statistician.
Answer: integral(-inf, inf) (g(x)*fx(x))dx
◉ Expected Value Property when X and Y are independent,.
Answer: E[XY] = E[X]E[Y]
◉ Variance.
Answer: Measure of "spread" of a distribution; standard deviation
squared; Var[X] = E[(X-mu)^2] = E[X^2] - (E[X])^2, where mu = E[X]
◉ Properties of Variance.
Answer: V(X)>=0, V(aX+b)=a^2V(X)
◉ True or False: Var[X+Y] = Var[X] + Var[Y].
, Answer: True *only* if X and Y are independent
◉ Covariance.
Answer: A measure of linear association between two variables.
Positive values indicate a positive relationship; negative values
indicate a negative relationship; E[XY] - E[X]E[Y]
◉ Correlation.
Answer: A measure of the extent to which two factors vary together,
and thus of how well either factor predicts the other.; Cov(X,Y) /
sqrt(Var(x)Var(Y))
◉ True or False: if Corr(X,Y) = 0 , then X and Y are uncorrelated..
Answer: True
◉ True or False: A random sample means that it is independent and
identically distributed..
Answer: True
◉ True or False: if E[xbar]=mu, then xbar is an unbiased estimator
of mu.
Answer: True
2026 PREMIUM QUESTIONS AND
SOLUTIONS
◉ Expected value of exponential distribution.
Answer: 1/lambda
◉ Law of the Unconscious Statistician.
Answer: integral(-inf, inf) (g(x)*fx(x))dx
◉ Expected Value Property when X and Y are independent,.
Answer: E[XY] = E[X]E[Y]
◉ Variance.
Answer: Measure of "spread" of a distribution; standard deviation
squared; Var[X] = E[(X-mu)^2] = E[X^2] - (E[X])^2, where mu = E[X]
◉ Properties of Variance.
Answer: V(X)>=0, V(aX+b)=a^2V(X)
◉ True or False: Var[X+Y] = Var[X] + Var[Y].
, Answer: True *only* if X and Y are independent
◉ Covariance.
Answer: A measure of linear association between two variables.
Positive values indicate a positive relationship; negative values
indicate a negative relationship; E[XY] - E[X]E[Y]
◉ Correlation.
Answer: A measure of the extent to which two factors vary together,
and thus of how well either factor predicts the other.; Cov(X,Y) /
sqrt(Var(x)Var(Y))
◉ True or False: if Corr(X,Y) = 0 , then X and Y are uncorrelated..
Answer: True
◉ True or False: A random sample means that it is independent and
identically distributed..
Answer: True
◉ True or False: if E[xbar]=mu, then xbar is an unbiased estimator
of mu.
Answer: True
