Question

Random variable X has mean 16 and standard deviation 9, random variable Y has mean 12 and standard deviation 7, the correlation between X and Y is 0.3.

How can we find the correlation between 4X - 5Y and 3Y - 1.

Answer #1

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

Suppose that X is a random variable with mean 21 and standard
deviation 4 . Also suppose that Y is a random variable with mean 42
and standard deviation 8 . Find the mean of the random variable Z
for each of the following cases
(Give your answer to three decimal places.)
a) Z = 3 + 10X
b) Z = 3X − 10
c) Z = X + Y
d) Z = X − Y
e) Z = −4X...

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...

The mean and standard deviation of a random variable x are 7 and
4 respectively. Find the mean and standard deviation of the given
random variables:
(1) y=x+1 μ= σ=
(2) v=8x μ= σ=
(3) w=8x+1 μ= σ=

A random variable ?x has a Normal distribution with an unknown
mean and a standard deviation of 12. Suppose that we take a random
sample of size ?=36n=36 and find a sample mean of ?¯=98x¯=98 . What
is a 95% confidence interval for the mean of ?x ?
(96.355,99.645)(96.355,99.645)
(97.347,98.653)(97.347,98.653)
(94.08,101.92)(94.08,101.92)
(74.48,121.52)

Consider independent random variables X and Y , such that X has
mean 2 and standard deviation 4, and Y has mean 1 and standard
deviation 9. Find the mean and standard deviation of the following
random variables. a) 3X b) Y + 6 c) X + Y d) X − Y e) X1 + X2,
where X1, X2 are independent copies of X.

(i) A binomial random variable has a mean equal to 187 and a
standard deviation of 12.
(a) Find the value of n. (Give your answer correct to the
nearest whole number.)
(b) Find the value of p. (Give your answer correct to four
decimal places.)
(ii) he probability of success on a single trial of a binomial
experiment is known to be 0.3. The random variable x,
number of successes, has a mean of 75.
(a) Find the number...

A random variable has a mean of 16 and standard deviation of 4.
Determine
(a) the mean and stan
dard deviation of the sample m
ean if the sample size is 100?
(b) the mean and standard deviation of
the sample mean if the sample size is 10,000?

Suppose X is a normal random variable with mean
μ = 100 and standard deviation σ = 7. Find
b such that
P(100 ≤ X ≤
b) = 0.3.
HINT [See Example 3.] (Round your answer to one decimal
place.)
b =

1. Given that the correlation between X and Y
is -0.48, the mean and standard deviation of X are 3.4 and 8.3, the
mean and the standard deviation of Y is 6.5 and 7.2 respectively.
Find the slope for the line of best fit.
2. Given that the correlation between X and Y
is -0.48, the mean and standard deviation of X are 3.4 and 8.3, the
mean and the standard deviation of Y is 6.5 and 7.2 respectively.
Find...

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