Question

2. 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

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