Question

The probability distribution for a random variable x is given in the table

X - -5 -3 -2 0 2 3

Probability- .17 .13 .33 .16 .11 .10

Find the probability that -2 < or equal to X < or equal to 2

Answer 1

`P(-2 \le x \le 2) =0.60`

Explanation:

Given

`\begin{array}{ccccccc}x & {-5} & {-3} & {-2} & {0} & {2} & {3} \ \\ P(x) & {0.17} & {0.13} & {0.33} & {0.16} & {0.11} & {0.10} \ \end{array}`

Required

`P(-2 \le x \le 2)`

From the distribution, the above is equivalent to:

`P(-2 \le x \le 2) =P(x = -2) +P(x = 0)+P(x = 2)`

We have:

`P(x = -2) = 0.33`

`P(x = 0)=0.16`

`P(x = 2) = 0.11`

So:

`P(-2 \le x \le 2) =P(x = -2) +P(x = 0)+P(x = 2)`

`P(-2 \le x \le 2) = 0.33 + 0.16 +0.11`

`P(-2 \le x \le 2) =0.60`