Question

Suppose there is a 10% chance of earning a grade of A in this course while the chance of earning a B is 20%, the chance of earning a C is 30%, the chance of earning a D is 15% and then of course there is the chance of failing. We will assign the random variable X the grade points earned when the course is completed with the corresponding grade; for example P(X = 4) = P(earn an A) = 0.10 after converting to a decimal number, P(X = 3) = 0.20 and so on.

a) Find P(X=0).

b) Give a table and draw a line graph showing the probability mass function of X.

c) Find E(X).

d) Find Var(X).

e. Find s.d.(X).

Answer 1

a)P(X=4)=1-(P(X=A)+P(X=B)+P(X=C)+P(X=D))=1-(0.1+02+0.3+0.15)=0.25

b)below is pmf of X:

Grade	x	f(x)	xP(x)	x2P(x)
fail	0	0.2500	0.000	0.000
D	1	0.1500	0.150	0.150
C	2	0.3000	0.600	1.200
B	3	0.2000	0.600	1.800
A	4	0.1000	0.400	1.600
		total	1.750	4.750
		E(x) =μ=	ΣxP(x) =	1.7500
		E(x2) =	Σx2P(x) =	4.7500
		Var(x)=σ2 =	E(x2)-(E(x))2=	1.6875
		std deviation=	σ= √σ2 =	1.2990

c)

E(X)=1.75

d)

Var(X)=1.6875

e)

SD(X)=1.2990

Answer 2

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answered by: certsout