Compute the standerd deviation?

Question

can some one please show me how to answer this problem. i an having trouble understanding how to do it. please use as much detale as possable.

compute the standerd deviation of the random variable x
x 0 1 2 3 4
p (x) 0.035 0.074 0.197 0.320 0.374

Answer 1

It's just a formula. There's not much understanding involved.

First you need the mean, which is "the expectation of X" and is given (for discrete probability distributions, as in the present case) by the sum, over all x, of x*p(x) Here, this sum is

(0)(0.035) + (1)(0.074) + (2)(0.197) + (3)(0.320) + (4)(0.374) = 2.924

so the mean is 2.924. This is often denoted µ.

A convenient formula for the variance (often denoted σ²), which is the square of the standard deviation, is the sum, over all x, of x² *p(x), minus µ². This is

(0²)(0.035) + (1²)(0.074) + (2²)(0.197) + (3²)(0.320) + (4²)(0.374) - 2.924²
= 1.176224

so the standard deviation σ is sqrt(1.176224) ≈ 1.0845