Question

Consider a bettering game where you bet $10 and have a probability of 0.45 of getting $20 back ($10 more than you started with) and a probability of 0.55 of getting no money back (losing the initial $10). The net amount of money gained on each trial is a discrete random variable. Losing money can be expressed as a negative gain.

(a) Draw a probability mass function representing this random variable.

(b) Find the expected value of this pmf.

(c) If you start with $50, what is the expected amount of money to be left with after playing 20 times?

please answer all thank you

Answer 1

a)

below is probability mass function of X :

P(X=10)=0.45

P(X=-10)=0.55

b)

expected value E(X)=xP(x) =0.45*10+0.55*(-10)= $ -1

c) expected amount of money to be left with after playing 20 times =E(50+20X)=50+20*E(X) =50-20*1 =$ 30