Need Help with parts a,b,c, and d please. Šta 241 11-8-17 Exam 2 Review Sheet Ex

Question

Need Help with parts a,b,c, and d please.

Šta 241 11-8-17 Exam 2 Review Sheet Exam 2 is November 16 and covers chapter 3 & 4 as discussed in lecture. Here are some problems that appeared on Exam 2, fall 2010. 1. A box contains replacement from the box and X is the sum of the values of the two coins, find: a penny, three nickels, and a dime. If two coins are selected at random without a) The probability function of X. b) The probability that X is at most 11 cents. c) The expected value ofX. d) The variance of X.

Explanation / Answer

1 a)

here P(X=6) =P(1penny and 1 nickel) =P(first penny and second nickel+first nickel and second penny)

=(1/5)*(3/4)+(3/5)*(1/4)=0.3

P(X=10) =P(2 nickels) =(3/5)*(2/4) =0.3

P(X=11) =P(1 penny and1 dime)=P(first penny and second dime+first dime and second penny)

=(1/5)*(1/4)+(1/5)*(1/4) =0.1

P(X=15) =P(1 nickel and 1dime)=P(first nickel and second dime+first dime and second nickel)

=(3/5)*(1/4)+(1/5)*(3/4) = 0.3

therfore below is probability function of X:

b) P(X<=11) =P(X=6)+P(X=10)+P(X=11) =0.3+0.3+0.1=0.7

c)

from above E(X)=10.40

d) Variance of X = 12.24

x p(x) 6 0.3000 10 0.3000 11 0.1000 15 0.3000

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