The standard deviation of Y (rounded to two decimal places) is:

Question

use the distribution of the random variable Y as show in this table to answer those questions:

 

Value            -4     0        2      6         9       11
Probability   .07    .13     .14     x        .29    .19

 

1. The missing probability value is:

 

2. P(Y < 3) is equal to:

 

3. The expectation of Y, E(Y), is:

 

4. The standard deviation of Y (rounded to two decimal places) is:

Answer 1

Ekene,

 

Calculations like these are best done in Excel so I'll just show you the method behind it.

 

1) total probability of all outcomes equals 1. So add up all the numbers and subtract from 1 to find x.

 

2) P(Y<3) is the sum of probabilities of X being -4,0 and 2. So add those numbers up for your answer.

 

3) E(Y) is the weighted sum of probabilities, so multiply each outcome by its probability and add up the numbers. In this case this is:

-4*P(-4)+0*P(0)+2*P(2)+6*P(6)+9*P(9)+11*P(11)

 

4) Standard deviation of Y is the square root of the variance of Y which weighs the distance each outcome is from E(Y). In this, subtract each outcome from E(Y), square that difference, and multiply that by its probability. You'll get six different numbers which you add up and then take the square root of the sum.

 

Again I don't recommend doing this with a calculator unless you're really careful. Good luck!