Assume that P(A₁ N A₂ NA3) > 0. Prove that P(A₁ NA₂ NÃ3 Ñ A4) = P(A1)P(A2|A1₁)P(A3|A1 N A₂)P(A4|A₁ ÑA₂ Ñ A3)

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: Suppose P(A) = 0.24 and P(B’ ) = 0.48   (a) Find P(A ∪ B) if A and B are independent. (b) Find…

A:

Q: Which of the following is not equal to P(100, 2)? 2P100 100! 98! 9900 100P2

A: We have given, P(100,2) The number of permutations of n things taken r at a time is defined as,…

Q: from x = 2 to x = 10 and x; is any value of x in Ex¡. Express lim s as a definite integral. n-x n D…

A:

Q: 7. Given P(A) = 1/3 and P(B) = 1/2 and P(A U B) = 2/3 . • (a) Find P(A¹) . . (b) Find P(A and B) (c)…

A: Given data, p(A) =13p(B)=12p(A∪B)= 23we have to find out the given probabilities.

Q: Suppose that 7 '(t) = and 7 (0) = . Find 7(t) 7(t) = <

A: Suppose that r→'t=12t,e0.2t,t and r→0=1,-1,4. Then we have to find r→t=?

Q: 1. Suppose P(A) = 4/10, P(B) = 5/10, and P(AB) = 2/10. (a) Compute P(AC). (b) Compute P(AUB). (c)…

A: As per our guidelines we are suppose to answer only three sub parts.…

Q: P(A)=0.02 and p(C)=0.07 determine p(A u C), given that A and C are independent

A: It is given that:And, A and C are independent events.

Q: (c) Check whether or not: Q (2¹/³) = Q(4¹/3) Also obtain (Q (2¹/³): Q].

A: We first find [Q(2^(1/3)):Q]  Then using this prove that Q(2^(1/3))=Q(4^(1/3))

Q: T 8-1 H = 2 1 & T = 6 5 Find T TB] (NO guess and check on linear combinations!)

A:

Q: Q2 (Bayes' Theorem) It is given that P(B|A) – 0,15. P (B|A) = 0.03 and P (A) = 06. Compute P(A|B).…

A: Ac=A bar  P(B/A)=0.15, P(B/Ac)=0.03, P(A)=0.60, P(A/B)=?

Q: X1 Xi + 2x3 , X1, X2, x3 ER – 4.x2 T: R³ → R², T x2 X3 - x3 ||

A: So first we prove that the given transformation is linear

Q: Let X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently. 1.…

A: X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently.

Q: Find S T(1– a²)+ 5* + 5m(1+ a²)| dæ.

A:

Q: (5) {1,2} C P({1, 2}).

A: Given  set is {1,2},  we knew that power set of a given set is set of all subsets of the given set.…

Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

A: