Let Y1 and Y2 be two independent identically distributed random variables with
nonzero variance. Which of the following statement is false:
Y1 - Y2 ≠ 0
E(Y1) - E(Y2) = 0
Var(Y1) - Var(Y2) = 0
Var(Y1-Y2) = 0
None of the above
Consider the distribution of annual salaries in a small firm. Suppose the mean salary is
$14,300 and the standard deviation of the salaries is $1,200. We know from the
Chebyshev inequality that the proportion of employees whose salaries fall outside the
range of $12,500 to $16,100 is
at most 1 / 2.25
at most 1 / 2.0
at most 1 / 1.5
at least 1 / 2.0
none of the above
Suppose that X and Y are two random variables, which may be dependent, and that
Var(X ) = Var(Y) . Assuming that 0 < Var(X + Y) < ∞ , and 0 < Var(X −Y) < ∞ .
Which of the following statement is true:
E(XY) = E(X )E(Y)
The random variable X + Y and X −Y are uncorrelated.
The random variable X + Y and X −Y are correlated.
None of the above
The average time that a programmer at an oil service company spends debugging
programs is 2.7 hours. The time spent debugging programs is considered to be
exponentially distributed. What is the probability that for any randomly selected
program, the programmer will spend between 1.5 hours and 2.5 hours debugging the
program?
If a hypothesis test leads to the rejection of the null hypothesis
A Type I error is always committed
A Type II error is always committed
A Type I error may have been committed only
A Type II error may have been committed only
Both Type I and II errors may have been committed
A pair-difference test is a
simple example of a chi-square goodness-of-fit test
simple example of a randomized block design
simple example of a completely randomized experiment
simple example of a chi-square homogeneity test
none of the above
A random variable with a F distribution
can assume only non-negative values
is the ratio of two chi-square random variables divided by their degrees of freedom
has an infinite expected value
has both (A) and (B) true
has none of the above true
Let μ and σ 2 be the mean and variance of population of the random variable X,
respectively. What is the variance of the random variable (X −μ ) /σ ?
1
μ /σ 2
4
σ 2
0
In a simple linear regression model Y = β0 +β1X +ε if a confidence interval for β1
spans the value of 0, one can conclude that
MSE = 0
R2 = 0
There is no linear statistical relationship between X and Y
There is no causal effect of X on Y but there may be a causal effect of Y on X
The regression function passes through the origin
Suppose the true model is Y = β0 +β1 X +εi , under what conditions the OLS estimate
of β is no longer unbiased.
E(εi ) ≠ 0
X is dependent of εi
Var(εi) ≠ σ2
εi is correlated with εj for i ≠ j
All of the above
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