a. Prove: If A and B are independent, then so are A and B.
b. Prove: If A and B are independent, then so are and .
c. Give an example of events A, B, and C such that
but
a. Prove: If A and B are independent, then so are A and B. b. Prove: If A and B are independent, then so are and . c. G...
Let A, B be events such that P(A) = 1/3 , P(B) = 1/4 , and P(AB) = 1/6. Find the following and write in words what events a)-d). Example: AB' means that either A occurs or B does not occur. HINT: draw a diagram. a) P(A' B') b) P(A' B) c) P(A' u B) d) P(A' B') We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
A pair of fair dice is tossed. Events A and B are defined as follows. A: The sum of the numbers on the dice is 5 B: At least one of the numbers 2 (a) Identify the sample points in the event P(A B). (b) Identify the sample points in the event P(A B). (c) Find P(A B). (d) Find P(A B). (e) Are A and B independent events? We were unable to transcribe this imageWe were unable to transcribe...
1. If P(A) = 0.4, P(B) = 0.6, P(C) = 0.3, P = 0.24, P = 0.15 and P(A U C) = 0.82. Which of the events A, B and C are independent? Give reasons for your answers. (A B) We were unable to transcribe this image
For two events, A and B, P(A) = 0.4 and P(B) = 0.35 a. If A and B are independent, find P(A B), P(A l B), P(A B). b. If A and B are dependent with P(A l B) = 0.6, find P(A B), P(B l A). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Using FTLM. a) Let . Use linear algebra to prove that there is a polynomial such that p + p' - 3p'' = q. Hint: consider the map defined by Tp: p + p' - 3p'', and use FTLM. b) Let be distinct elements of . Let be any elements of . Use linear algebra to prove that there is a such that Hint: consider the map defined by . You can use any facts from algebra about the solution...
Prove, or give a counter example to disprove the following statements. a) b) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
1. a) Prove: if and , then b) State the converse above, and find a counterexample to the converse above. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let E and F be events for which P(E) = .5, P(F)= .4, and P(E F) = .2 a) are E and F mutually exclusive or independent? (justify mathematically) b) Find P(E F) c) Find P(F') d) Find P(F l E) e) Find P(E' F) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Suppose is a bounded function for which there exists a partition such that . Prove: is a constant function f : a, b] →R We were unable to transcribe this imageL(P, f,a) = U(P, f,a) We were unable to transcribe this image
Suppose X and Y are independent and Prove the following a) U=X+Y~gamma(α + β,γ) b) V=X/(X + Y ) ∼ beta(α,β) c) U, V independent d) ~gamma(1/2, 1/2) when W~N(0,1) X ~ gammala, y) and Y ~ gamma(6, 7) We were unable to transcribe this image