Question 1

Which of the following statements is true of the standard normal distribution,but not other normal probability distributions? A)P(X<0)=0.5 B)it is symmetric C)P(X<($\mu$_x-1))= P(X>($\mu$_x+1)) D)it is often referred to as a "bell" curve

Accepted Answer

The standard normal distribution is centered at 0, making P(X<0) = 0.5 unique to it, whereas other normal distributions are centered at different means (μ). Options B and D describe characteristics common to all normal distributions, and option C is unclear due to formatting errors.

Question 2

Which of the following statements about the standard normal distribution is NOT true? A)$\mu$=0 ,$\sigma$² = 1 B)it can be used to find probability intervals for any normal distribution C)it is symmetric D)it is derived from repeated sampling of naturally occurring phenomena

Accepted Answer

The standard normal distribution is not derived from repeated sampling of naturally occurring phenomena, but rather is a theoretical distribution with a specific mean of 0 and standard deviation of 1. It is often used as a reference distribution to standardize other normal distributions.

Question 3

Which of the following is NOT equal to cov(X,Y)? A)$\mu$_xy B)E[(x-$\mu$_x)(y-$\mu$_y)] C)E(xy)-$\mu$_x$\mu$_y D)$\rho$_xy

Accepted Answer

The covariance, cov(X,Y), is defined as E[(X-μx)(Y-μy)] or E(XY) - μxμy. Option D represents the correlation coefficient, not the covariance.

Question 4

The expected value of a random variable is&#10;A)the probability weighted mean&#10;B)a measure of central tendency of the pdf&#10;C)average value that occurs in many repeated trial of an experiment&#10;D)all of the above

Accepted Answer

The expected value of a random variable is the probability weighted mean, which is a measure of central tendency of the pdf. It is also the average value that occurs in many repeated trials of an experiment. Therefore, all of the above options are correct.

Question 5

)The difference between a pdf and cdf is ___________________________.

Accepted Answer

The answer of )The difference between a pdf and cdf...

Question 6

How would you write the following expression using summation notation? Q₁ + Q₂ + Q₃ + Q₄ + …………..+ Q₂₉

Accepted Answer

The answer of How would you write the following expression...

Question 7

A measure of the daily change in the closing value of the DJIA is a ____________ variable and a variable indicating whether it moved up or down is a ______________ variable.&#10;A)continuous,discrete&#10;B)flow,stock&#10;C)random,determined&#10;D)discrete,continuous

Accepted Answer

The daily change in the closing value of the DJIA is a continuous variable because it can take on any value within a range (including decimals). The variable indicating whether it moved up or down is a discrete variable because it has a finite number of categories (up or down).

Question 8

If (P(X=x|Y=y)= P(X=x),then&#10;A)Y is the dependent variable&#10;B)X and Y are positively correlated&#10;C)X and Y are statistically independent&#10;C) )Y must be a discrete random variable

Accepted Answer

If P(X=x|Y=y)= P(X=x), then X and Y are statistically independent, meaning that the occurrence of one does not affect the occurrence of the other. This does not necessarily mean that Y is the dependent variable or that X and Y are positively correlated, and Y can be either a discrete or continuous random variable.

Question 9

If Z is a random variable generated by adding together X and Y which are also random variables,what do we know about var(Z)if X and Y are positively correlated.?&#10;A)var(Z)= var(X)+ var(Y)&#10;B)var(Z)< var(X)+ var(Y)&#10;C)var(Z)> var(X)+ var(Y)&#10;D)var(Z)= var(X)* var(Y)

Accepted Answer

When X and Y are positively correlated, they tend to move together in the same direction. Therefore, when added together to form Z, they amplify each other's effect on the variance. This leads to the variance of Z being greater than the sum of the variances of X and Y, i.e., var(Z) > var(X) + var(Y).

Deck 2: Pp : Prob, Probability Primer, Probability Primer