Question

A random variable X is normally distributed with a mean of 100 and a variance of 100, and a random variable Y is normally distributed with a mean of 180 and a variance of 324. The random variables have a correlation coefficient equal to −0.4. Find the mean and variance of the random variable below.W=2X−4Y

μW=

(Type an integer or a decimal.)

σ2W=

(Type an integer or a decimal.)

Answer #1

A random variable X is normally distributed with a mean of 121
and a variance of 121, and a random variable Y is normally
distributed with a mean of 150 and a variance of 225. the random
variables have a correlation coefficient equal to 0.6. Find the
mean and variance of the random variable :
W= 6X + 3Y

Let X be a random variable with a mean of 9 and a variance of
16. Let Y be a random variable with a mean of 10 and a variance of
25. Suppose the population correlation coefficient between random
variables X and Y is -0.4.
a) Find the mean of the random variable W = 3X - 5Y.
b) Find the standard deviation of the random variable Z = X +
Y

X is a normally distributed random variable with a mean of 100
and a variance of 144. Use Excel to find the value
of X that gives a probability of 10% on the right.
In other words, find Xo such that P(X > Xo) =
0.10. Write your answer to 4 decimal places.
A.
115.3672
B.
115.3786
C.
115.3600
D.
115.3721

Suppose X is a normally distributed random variable with mean μ
= 10 and variance σ2 = 4. Find P(9 < X < 12).

The sum of independent normally distributed random variables is
normally distributed with mean equal to the sum of the individual
means and variance equal to the sum of the individual variances. If
X is the sum of three independent normally distributed random
variables with respective means 100, 150, and 200 and respective
standard deviations 15, 20, and 25, the probability that X is
between 420 and 460 is closest to which of the following?

a random variable, X, is normally distributed with a mean of 100
and a standard deviation of 6.
What is the probability, Pr(X<100)? Answer Please use 4
significant digits
What is the probability, Pr(X>116)? Answer Please use 4
significant digits
What is the probability, Pr(90<X<110)? Answer Please use 4
significant digits

Given independent random variables with means and standard
deviations as shown, find the mean and standard deviation of each
of these variables:
Mean
SD
a) 4X
b) 4Y+3
c) 2X+5Y
X
70
14
d) 5X−4Y
e) X1+X2
Y
10
5
a) Find the mean and standard deviation for the random variable
4X.
E(4X)=_____________
SD(4X)=_______________
(Round to two decimal places as needed.)
b) Find the mean and standard deviation for the random variable
4Y+3.
E(4Y+3)= ________________
SD(4Y+3)= _____________________
(Round to...

1.Suppose X is a random variable that is normally distributed with mean 5 and standard deviation 0.4. If P (X≤X0) = P (Z≤1.3). What is the value of X0.?
Select one:
2.00
5.52
6.90
4.48
2.Suppose X is a random variable that is normally distributed with a mean of 5. If P (X≤3) = 0.2005, what is the value of the standard deviation?
Select one:
σ = 2.38
σ = −2
σ = 1.38
σ = 2

Assume the random variable X is normally distributed with a mean
μ = 50 and standard deviation σ = 4.5. Find the P (x > 60)
(three-decimal accuracy) Find the P (35 < x < 55)
(three-decimal accuracy) Find x so that the area below x is .12.
(one-decimal accuracy)

A random variable X is normally distributed. Suppose we obtain a
random sample of 11 elements from the population. Further assume
that the population variance is 100. Find the probability that the
sample variance is at least 48.6.

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