Dylan asks for his lunch money every day from his mother. There is an 80% chance

Question

Dylan asks for his lunch money every day from his mother. There is an 80% chance she has money to give him and if so, he gets $5. However, if she does not have money Dylan has to give her $2. Whether Dylan gets $5 or gives out $2 is independent from day to day. Let x equal the number of times Dylan gets money during a 5-day week. Let w = the total amount he gets/gives for lunch in a week. (When he gives money just make the amount negative.)

a. As a function of x, what is w?  
b. What is the expected value of x?  
c. What is the expected value of w?  
d. What is the probability that x = 5?  

Explanation / Answer

a)

x = the number of times Dylan gets money during a 5-day week.

w = the total amount he gets/gives for lunch in a week.

b) b. What is the expected value of x? .

E(x) =lamda = n * P

= 5 *days * 0.80

=4

So the expected value of x is 4.

C. What is the expected value of w?

E(W) = Sum (W * P(W))

=(5*0.80 -0.20*2)

=3.6

d. What is the probability that x = 5?

here n=5 days P=0.80 and we want to find X=5

P(X=5) = nCx Px * (1-P)n-x

=5C5 * (0.80)5 * (0.20)0

= 0.3278

So the probability of X=5 is 0.3278 .

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