Question

pls look at attached picture i have tried asking many and no one can explain it to me

Answer 1

Answer: a = 0.98

Explanation: For this case we have the following table:

x | P(x)

0| 0.1296

1| 0.3456

2| 0.3456

3 | 0.1536

4| 0.0256

We can find the expected value as:

E(X)= 0*0.1296 + 1*0.3456+ 2*0.3456+ 3*0.1536+ 4*0.0256= 1.6

Now we can find the second moment like this:

E(X^2)= 0^2*0.1296 + 1^2*0.3456+ 2^2*0.3456+ 3^2*0.1536+ 4^2*0.0256= 3.52

And the variance is given by:

Var(X)= E(X^2)- [E(X)]^2 = 3.52 -(1.6^2)=0.96

Then the standard deviation is:

Sd(X)= sqrt(0.96)=0.98