Let X₁ och X₂ be two independent binomial distributed variables, where X₁ Bin(2, 0.3) and X₂ Bin(2, 0.5). Let U= max{X₁, X2}and let V= min(X₁, X₂). a. Determine the probability P(U-V) b. Determine the simultaneous distribution p(x)=P(U=u, V=v). c. Determine the conditional distribution P(VIU) of V given U. (State the conditional mass function p(v|u).)

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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Let X, och X, be two independent binomial distributed variables, where X, Bin(2, 0.3) and
X2~Bin(2, 0.5). Let U= max{X1, X2}and let V= min(X1, X2).
a. Determine the probability P(U=V)
b. Determine the simultaneous distribution p(ux)=P(U=u, V=v).
c. Determine the conditional distribution P(V|U) of V given U. (State the conditional mass
function p(v|u).)
Transcribed Image Text:Let X, och X, be two independent binomial distributed variables, where X, Bin(2, 0.3) and X2~Bin(2, 0.5). Let U= max{X1, X2}and let V= min(X1, X2). a. Determine the probability P(U=V) b. Determine the simultaneous distribution p(ux)=P(U=u, V=v). c. Determine the conditional distribution P(V|U) of V given U. (State the conditional mass function p(v|u).)
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