Question

The random variable X has the following probability mass function.X -1 0 2 6 7P(x) 0.3 0.1 0.3 0.2 0.1Answer the next 4 questions.5. Find the probability P( -1 < X ≤ 2) = ______6. Find the cumulative distribution function F(x) and calculate F(3.2) = _____________7. E(X) = ___________8. Var(X) = __________

Answer 1

Explanation:

Given that X has the following pdf.

x -1 0 2 6 7 Total

P(X) 0.3 0.1 0.3 0.2 0.1 1

xP(X) -0.3 0 0.6 1.2 0.7 2.2

x^2P(X) 0.3 0 1.2 7.2 4.9 13.6

Var(x) 13.6-2.2^2 8.76

Std dev 2.959729717

5)
`P( -1 < X ≤ 2) = P(0)+P(2)\\= 0.1+0.3=0.4`

6. Find the cumulative distribution function F(x) and calculate F(3.2) =

x -1 0 2 6 7

P(X) 0.3 0.1 0.3 0.2 0.1

F(x) 0.3 0.4 0.7 0.9 1

F(3.2) = P(X<3.2) = ___F(X<6) = 0.7__________

7. E(X) = ______2.2_____

8. Var(X) = ____8.76______