4, Suppose P(A) 2 0.8 and P(B) > 0.5. Prove P(AN B) > 0.3. Hint: You may use P(AUB)< 1.

Q: Given X~ N(20,16), find c. P( 19 < X<23) (4 decimal place)

A: X~N(20,16) Mean(μ)=20 Variance(σ2)=16 standard deviation(σ)=16=4

Q: Q2/Let X-N(4,9). Find (a) P(1 2). (c) P(|X-21 >5)

A:

Q: When P(w) = 9w² + lw + 3, evaluate P( – 5) P( – 5) =

A: We have p(w), so to find p(—5) put w=—5 in the expression of p(w)

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: Consider a small shop with only one checkout counter. The arrivals of customers are distributed…

A: Solution Dear student as per guidelines we answer the first question only when multiple questions…

Q: If B C A, then (i) P(AB)=P(A) - P(B), (ii) P(B) ≤ P(A)

A:

Q: Find 1 (9) Lp(p – 1). p(p²-1)3 (10) L-1 (p2+1)2,

A:

Q: IfX~N(7,4), the P(15.364 ≤ (X-7)² ≤ 20.095) is

A: Given problem is :

Q: It is given that X~N( 30, 5). Find P(27<X<33)

A:

Q: Suppose P(A) = 0.4 and P(B) and B, show that 0.1 ≤ P(An B) ≤ 0.4. = 0.7. With no other assumptions…

A: We have given thatP(A) = 0.4P(B) = 0.7We have to show that0.1 ≤ P(AB) ≤ 0.4

Q: If S= {a,b,c} with P(a)= 2P(b)= 4 P(c), find P(a)

A:

Q: Q2/ Let X-N(4,9). Find (a) P(1 2). (c) P(|X2| >5)

A:

Q: Let 7(t) Find (Note that the +C has already been included for you). = + Č Answer preview: <

A:

Q: If Z ~ N(0,1) what is P(-0.83 < Z < 1.06):

A:

Q: It is given that X~N(30,5). Find P(27<X<33)

A: Given : X~N(30,5)

Q: Calculate P(z<-1.2)

A: The z-score is standard normal variable with mean 0 and standard deviation 1.

Q: SupposethatAandBaretwoindependenteventswithP(A) = 0.3andP(B) = 0.3. Calculate(a) P(A and B) (b) P(A…

A:

Q: P (Z<1.8572)

A: Answer - Find   P (Z&lt;1.8572)

Q: If k = (0.0003,-0.0012, 0.0015,-0.0014) in R4 then -5.2||||=0.0062

A:

Q: Suppose that P(A) = 0.1, P(B) = 0.3, and P(A|B) + P(B|A) = 0.8. Find P(A ∩ B).

A: From the information, given thatThe formula of the conditional probability, for any two events…

Q: Compute x3 in two ways: by computing x, and x2, and by computing P³ [1] P= x₁ = 0.1 0.2 0.9 0.8 0.19…

A: Solution: The given matrix is, P=0.10.20.90.8,x0=10. Now compute x3 in two ways:

Q: P(X) = 0.62, P(Y) = 0.28, P(X and Y) = 0.16. Find P(not YIX). O none of the above 0.4129 0.5714…

A:

Q: If X: N(132,100) find P(122<X<142)

A: Given : X follows a Normal distribution  with Mean  = 132 Variance  = 100 Standard deviation  = √…

Q: 10. Suppose X-N (3.2) Find P (22}, P(X>3)

A: Given that v  X ~ N ( 3, 22 )  i.e. μ = 3 ? = 2 By using standard normal distribution we solve this…

Q: Problem 7. when Compute the joint pdf of Z = X² + y², W = 2Y, fxy(x, y) = 1 2πσ2 e-[(x²+y²)]/20²

A:

Q: P(z ≤ 2.37)

A:

Q: Let P(x) denote the statement "x < 4." P(4) is A) True False

A:

Q: B Given that p(A| B)=0, and p(A)=.15, are A and B (a) independent? (b) exclusive?

A: Ans#- Given, P(A | B) = 0, and P(A) = 0.15.            Are A and B        (a) Independent?…

Q: P(0.74<Z<2.11)

A: Let Z be the standard normal variable with parameters μ=0  and σ=1 The probability is,

Q: An employee of a car parts store was mistaken and saved the defective flashlights, along with the…

A: Probability quantifies the chances of happening an event. The probability values always lie in the…

Q: P(A) = 0.5, P(B) = 0.3, P(A ∩ B)= 0.1 a) Find P(A given B).   b) P(B|A)

A: As per given by the question, there are P(A) = 0.5, P(B) = 0.3,and P(A ∩ B)= 0.1., then find PA…

Q: ccording to a​ study, 58​% of all males between the ages of 18 and 24 live at home. ​ (Unmarried…

A: n = 226 x= 152 p = 0.58

Q: Suppose X - U(2, 7). Determine P(X > 6 | X > 5). Note: This is a very challenging problem.

A: