Jordan is practicing field goals. On each attempt, he have a 0.35 chance of making it. Let X be the number of attempts he needs to make five successful attempts. (a) What is E[X]? (b) What is E[X2]? (Hint: Use the variance instead of finding this directly.) (c) What is P[10 ≤ X ≤ 15]?

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Jordan is practicing field goals. On each attempt, he have a 0.35 chance of making it. Let X be the number of attempts he needs to make five successful attempts.
(a) What is E[X]?
(b) What is E[X2]? (Hint: Use the variance instead of finding this directly.)
(c) What is P[10 ≤ X ≤ 15]?

Expert Solution
Step 1

It is given that n=5 and p=0.35.

(i) 
EX=n×p=5×0.35=1.75

Step 2

(ii)
VX=n×p×1-p=2×1-0.35=1.3

 

It is known that, VX=EX2-EX2.

So,
EX2=VX+EX2=1.3+1.752=1.3+3.0625=4.3625

 

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