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Chapter 10 practice bank

100 questions:
Distributions

Solve on paper first. Reveal only the final answer when you want to check yourself. There are no worked solutions in this bank by design.

34 easy 33 medium 33 advanced

EasyExpected valuerandom-variables-distributions-1

X equals 0 with probability 8/10 and 4 with probability 2/10. Find E[X].

EasyBernoulli momentsrandom-variables-distributions-2

For X~Bernoulli(2/10), find E[X] and Var(X).

EasyBinomial momentsrandom-variables-distributions-3

For X~Binomial(8,2/10), find E[X] and Var(X).

EasyLinearity of expectationrandom-variables-distributions-4

If E[X]=2, find E[2X+3].

EasyVariance scalingrandom-variables-distributions-5

If Var(X)=2, find Var(2X+9).

EasyCDFrandom-variables-distributions-6

X has P(X=0)=1/10, P(X=1)=4/10, and the remaining mass at X=2. Find F(1).

EasyUniform meanrandom-variables-distributions-7

If X is uniform on [0,10], find E[X].

EasyStandardizationrandom-variables-distributions-8

A distribution has mean 40 and standard deviation 5. Find the z-score of x=45.

EasyExpected valuerandom-variables-distributions-9

X equals 0 with probability 7/10 and 5 with probability 3/10. Find E[X].

EasyBernoulli momentsrandom-variables-distributions-10

For X~Bernoulli(3/10), find E[X] and Var(X).