Question

Consider the probability distribution shown below. x 0 1 2 P(x) 0.15 0.80 0.05 Compute the expected value of the distribution. (Enter a number.) Compute the standard deviation of the distribution. (Enter a number. Round your answer to four decimal places.)

Answer 1

Answer:

Expected value =0.9

Standard deviation = 0.4359

Step-by-step explanation:

Let's use the formula to find expected value or mean.

Expected value =Σ x *P(x)

  x    0    1     2

P(x) ) .15  .8  .05

So, expected value = (0)(0.15) +1(0.8)+2(0.05)

                                = 0 +0.8 +0.1

                                =0.9

Expected value =0.9

Now, let's find standard deviation

x           $(x- E(x))^{2}$         $(x-E(x))^{2} *p(x)$

0           $(0-0.9)^{2}$            $(0-0.9)^{2} *0.15$  =0.1215

1            $(1-0.9)^{2}$            $(1-0.9)^{2} *0.8$    =0.008

2           $(2-0.9)^{2}$             $(2-0.9)^{2} *0.05$  =0.0605

Now, add the last column together and then take square root to find standard deviation.

Standard deviation of the distribution =$\sqrt{0.1215+0.008+0.0605)}$

Simplify it, so standard deviation =0.4358898...

Round the answer to nearest four decimal places

Standard deviation = 0.4359