Question

Use the following table to answer the questions. a) Find the probability that X is at...

  1. Use the following table to answer the questions.

    1. a) Find the probability that X is at most -50.

    2. b) Find the probability that X is more than -10.

    3. c) Find the probability that X is between (inclusive) -90 and 0.

    4. d) Construct the corresponding pdf.

    5. e) Calculate the variance of X.

x. -100. -80. -40. 0. 10

P(X_<x) 0.35. 0.43. 0.64. 0.87. 1

0 0
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Answer #1

from given table

a)

P(X<=-50)=P(X=-80)=0.43

b)P(X>-10)=1-PX<= -10)=1-0.87=0.13

c)

P(-90 <=X<=0)=P(X<=0)-P(X<=-100)=0.87-0.35=0.52

d)

below is pmf of X:

x P(x)
-100 0.35
-80 0.08
-40 0.21
0 0.23
10 0.13

e)

x P(x) xP(x) x2P(x)
-100 0.35 -35.000 3500.000
-80 0.08 -6.400 512.000
-40 0.21 -8.400 336.000
0 0.23 0.000 0.000
10 0.13 1.300 13.000
total -48.500 4361.000
E(x) =μ= ΣxP(x) = -48.5000
E(x2) = Σx2P(x) = 4361.0000
Var(x)=σ2 = E(x2)-(E(x))2= 2008.750

variance of X =2008.75

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