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The cumulative probability distribution shows the probability: correct answers that a random variable is less than or equal to a particular value. The correlation between X and Y: correct answers can be calculated by dividing the covariances between X and Yby the product of the two standard devi...

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  • September 10, 2024
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Econometrics || Already Graded A+.
The cumulative probability distribution shows the probability: correct answers that a random
variable is less than or equal to a particular value.

The correlation between X and Y: correct answers can be calculated by dividing the covariances
between X and Yby the product of the two standard deviations.

Var(aX + bY ) is correct answers a2σX2 +2abσXY +b2σY2

Assume that Y is normally distributed N(μ,σ2). To find Pr(c1 ≤ Y ≤ c2), where
c1 <c2,anddi =ci−μ,youneedtocalculatePr(d1 ≤Z≤d2)= correct answers Φ(d2 ) − Φ(d1 )

The Student t distribution is: correct answers the distribution of the ratio of a standard normal
random variable, divided by the square root of an independently distributed chi−squared random
variable with m degrees of freedom divided by m.

When there are ∞ degrees of freedom, the t∞ distribution: correct answers equals the standard
normal distribution.

A box has 20 screws, three of which are known to be defective. What is the probability that the
first two screws taken out of the box are both defective? correct answers 0.0158

The probability of stock A rising is 0.3; and of stock B rising is 0.4. What is the probability that
neither of the stocks rise, assuming that these two stocks are independent? correct answers 0.42

A bag has five pearls in it, out of which one is artificial. If three pearls are taken out at random,
what is the probability that the artificial pearl is one of them? correct answers 3/5

Given the following probability distribution:
X P(X) 1 0.2
2 0.3
3 0.3
4 0.2
What is the variance of the random variable X? correct answers 1.05

The expected value of a discrete random variable: correct answers is computed as a weighted
average of the possible outcome of that random variable, where the weights are the probabilities
of that outcome.

Let Z be a standard normal random variable. Find Pr(-0.5 < Z < 0.5). correct answers 0.3830

Find the probability that a standard normal random variable has a value greater than -1.56.
correct answers 0.9406

, Let X be a normally distributed random variable with mean 100 and standard deviation 20. Find
two values, a and b, symmetric about the mean, such that the probability of the random variable
being between them is 0.99. correct answers 48.5, 151.5

A spark plug manufacturer believes that his plug lasts an average of 30,000 miles, with a
standard deviation of 2,500 miles. What is the probability that a given spark plug of this type will
last 37,500 miles before replacement? Assume a normal distribution. correct answers 0.0013

Let Y be a random variable with mean μY . Then var(Y ) equals: correct answers E[(Y − μY )2].

The conditional expectation of Y given X, E[Y |X = x], is calculated as follows: correct answers
Eki=1 yi Pr(Y = yi|X = x).

X and Y are two random variables. Which of the following statements holds true regardless of
whether X and Y are independently distributed? correct answers E(Y ) = E[E(Y |X)]

Which of the following statements is correct? correct answers SST = SSE + SSR

In the simple linear regression model
y = β0+β1x+u E (u|x) = 0
the regression slope correct answers indicates by how many units the conditional mean of y
increases, given a one unit increase in x.

The OLS estimator is derived by correct answers minimizing the sum of squared residuals.

In the simple regression model y = β0 + β1x + u, the simple average of the OLS residuals is
correct answers zero

In the simple regression model y = β0 + β1x + u, to obtain the slope estimator using the least
squares principle, you divide the correct answers sample covariance of x and y by the sample
variance of x.

The OLS slope estimator, β1, has a smaller standard error, other things equal, if correct answers
there is more variation in the explanatory variable, x

Let y be the fitted values. The OLS residuals, u , are defined as follows: correct answers y −y₋

The error term is homoskedastic if correct answers V ar(u|x) is constant

Under the assumption of the Gauss-Markov Theorem, in the simple linear regres- sion model, the
OLS estimator is BLUE. This means what? correct answers The OLS estimator is the estimator
that has the smallest variance in the class of linear unbiased estimators of the parameters.

The proof that OLS is BLUE (Gauss-Markov Theorem) requires all of the following assumptions
with the exception of: correct answers the errors are normally distributed.

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