Suppose that X is a random variable with mean 30 and standard deviation 4. Also suppose that Y is a random variable with mean 50 and standard deviation of 8. Assume that the correlation between X and Y is zero.
1. Find the variance and the standard deviation of the random variable Z for each of the following cases. Show work.
(a) Z = 35 -10X
(b) Z = 12X - 5
(c) Z = X +Y
(d) Z = X -Y
(e) Z = -2X + 2Y

(a) The variance and standard deviation of Z = 35 - 10X are 1600 and 40 respectively.

(b) The variance and standard deviation of Z = 12X - 5 are 2304 and 48 respectively.

(c) The variance and standard deviation of Z = X + Y are 80 and 8.94 respectively.

(d) The variance and standard deviation of Z = X - Y are 80 and 8.94 respectively.

(e) The variance and standard deviation of Z = -2X + 2Y are 320 and 17.89 respectively.

Step-by-step explanation:

The random variable X has mean and standard deviation as follows:

The random variable Y has mean and standard deviation as follows:

It is provided that the correlation between X and Y is 0.

This implies that Cov (X, Y) = 0.

(a)

Compute the variance of Z = 35 - 10X as follows:

Then the standard deviation of Z = 35 - 10X is:

Thus, the variance and standard deviation of Z = 35 - 10X are 1600 and 40 respectively.

(b)

Compute the variance of Z = 12X - 5 as follows:

Then the standard deviation of Z = 12X - 5 is:

Thus, the variance and standard deviation of Z = 12X - 5 are 2304 and 48 respectively.

(c)

Compute the variance of Z = X + Y as follows:

Then the standard deviation of Z = X + Y is:

Thus, the variance and standard deviation of Z = X + Y are 80 and 8.94 respectively.

(d)

Compute the variance of Z = X - Y as follows:

Then the standard deviation of Z = X - Y is:

Thus, the variance and standard deviation of Z = X - Y are 80 and 8.94 respectively.

(e)

Compute the variance of Z = -2X + 2Y as follows:

Then the standard deviation of Z = -2X + 2Y is:

Thus, the variance and standard deviation of Z = -2X + 2Y are 320 and 17.89 respectively.

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

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step-by-step explanation: