Question

The probability distribution of a random variable X is given. 2 0 -2 -4 X 0.3 0.1 0.3 0.1 0.2 P(X=x) Compute the mean, variance, and standard deviation of X. (Round your answers to two decimal places.) mean variance standard deviation

Answer 1

Answer:

$\mu=0.4$

$V=8.64$

$\sigma=2.94$

Step-by-step explanation:

Given : The probability distribution of a random variable X.

To find : The mean, variance, and standard deviation of X.

Solution :

First we create the table as per requirements,

x      P(x)         xP(x)           x²            x²P(x)

4     0.3           1.2              16              4.8

2     0.1            0.2             4               0.4

0     0.3            0               0                0

-2    0.1           -0.2             4               0.4

-4    0.2          - 0.8            16              3.2

   ∑P(x)=1     ∑xP(x)=0.4               ∑x²P(x)=8.8

1) The mean of x is defined as

$\mu=\sum xP(x)=0.4$

2) The variance of x is defined as

$V=\sum x^2P(x)-(\sum xP(x))^2\\V=8.8-(0.4)^2\\V=8.8-0.16\\V=8.64$

3) The standard deviation of x is defined as  

$\sigma=\sqrt{V}\\\sigma=\sqrt{8.64}\\\sigma=2.94$