Question

A discrete random variable named X has the following pmf (probability mass function):

X	P(x)
1	0.6
3	0.2
7	0.1
11	0.1

17a) Find P(X>6)

17b) What is the probability two independent observations of X will both equal 1?

17c) Find the population mean also known as E(X)= the expected value of

17d) Find the population variance of X with both the “regular” formula and “convenient”

formula

Make a table and show your work. You should get the same answer with both

formulas. Finally, find the standard deviation.

Answer 1

a)

P(X>6) = P(X=7) + P(X=11) = 0.1+0.1 = 0.2

b)

P(Two independent observations will both equal 1) = P(X=1) * P(X=1) = 0.6*0.6 = 0.36

c)

d)

Using convenient formula:

Using the standard formula:

X	p(X)	X * p(x)	X-E(x)	(X-E(x))^2	((X-E(x))^2)*p(x)
1	0.6	0.6	-2	4	2.4
3	0.2	0.6	0	0	0
7	0.1	0.7	4	16	1.6
11	0.1	1.1	8	64	6.4
				84	10.4

Var(X) =

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