discrete math, need help with 1 & 2 1. (6 points) Consider a lottery game in whi

Question

discrete math, need help with 1 & 2

1. (6 points) Consider a lottery game in which you choose 5 distinct numbers from 1 to 50. Later someone will randomly pick 5 distinct numbers for an "official draw" (a) What is the probability that all 5 numbers in the official draw match the numbers that you picked (order of them being drawn does not matter)? num numbers that you picked? 2. (6 points) Suppose that a random variable X can take on the values 1, 2, 3, and 4, and suppose that the following is the CDF is the following: F(1) 0.2, F(2) 45, F(3) 75, F(4) 1. (a) What is the PMF of X? That is, give the following values: P(X 1), P(X 2),P(x 3), and P(X = 4) (b) What is E(X)? (c) What is V(X)?

Explanation / Answer

Ans:

2)

a)

p(1)=0.2,p(2)=0.25,p(3)=0.3,p(4)=0.25

b)E(X)=Mean=2.6

c)V(X)=Variance=1.14

x 1 2 3 4 Total F(x)= 0.2 0.45 0.75 1 p(x)= 0.2 0.25 0.3 0.25 x.p(x)= 0.2 0.5 0.9 1 2.6 (x-2.6)^2*p(x) 0.512 0.09 0.048 0.49 1.14

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