Question

What is the standard deviation of a random variable q with the following probability distribution? (Do not round intermediate calculations. Enter your answer in numbers not in percentage. Round your answer to 4 decimal places.) Value of q Probability 0 0.25 1 0.25 2 0.50

Answer 1

Answer:

The standard deviation of given probability distribution is 0.8292

Step-by-step explanation:

We are given the following in the question:

              q:        0          1          2

Probability:    0.25     0.25    0.50

Formula:

$E(q) = \displaystyle\sum q_ip(q_i)\\=0(0.25) + 1(0.25) + 2(0.50) = 1.25$

$E(q^2)= \displaystyle\sum q_i^2p(q_i)\\=0^2(0.25) + 1^2(0.25) + 2^2(0.50) = 2.25$

Variance =

$\sigma^2 = E(q^2) = (E(q))^2\\= 2.25- (1.25)^2\\=0.6875\\\sigma = \sqrt{0.6875} = 0.8292$

Thus, the standard deviation of given probability distribution is 0.8292