Answered

IDNLearn.com: Your go-to resource for finding expert answers. Discover detailed answers to your questions with our extensive database of expert knowledge.

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.)

Sagot :

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           [tex](x- E(x))^{2}[/tex]         [tex](x-E(x))^{2} *p(x)[/tex]

0           [tex](0-0.9)^{2}[/tex]            [tex](0-0.9)^{2} *0.15[/tex]  =0.1215

1            [tex](1-0.9)^{2}[/tex]            [tex](1-0.9)^{2} *0.8[/tex]    =0.008

2           [tex](2-0.9)^{2}[/tex]             [tex](2-0.9)^{2} *0.05[/tex]  =0.0605

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

Standard deviation of the distribution =[tex]\sqrt{0.1215+0.008+0.0605)}[/tex]

Simplify it, so standard deviation =0.4358898...

Round the answer to nearest four decimal places

Standard deviation = 0.4359

We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.