Question

if am and cv of a random variable x are 10 & 40 respectively , then the variance of( -15+3x/2)​

Answer 1

Variance of $(-15+\frac{3x}{2})$ is 36

Step-by-step explanation:

1) We have,

$\mu = 10\\ \\ CV = 40\%=0.4\\ \\=>\frac{\sigma}{\mu}=0.4\\ \\ =>\sigma=4$

Hence, the variance of random variable X is 4^2 = 16

2) Now, Coming to the question

Using the property :

$Var(a+bX)=b^2Var(X);\quad a,b\in R$

$Var(-15+\frac{3X}{2})=(\frac{3}{2})^2Var(X)\\ \\=\frac{9}{4}Var(X)\\ \\=\frac{9}{4}*16=36$

Then,

Variance of Random Variable X is 36.

I took CV in percent form otherwise 40 is too large value for Coefficient of variation.

Answer 2

the answer to your question is given below:

Variance of Random Variable X is 36.

Thx