assume that Pr[A∪B]=0.6 and Pr[A]=0.2 (1) What is Pr[B] if A and B are independent events?

Q: Let X - Unif(0, 2) and Y - Unif(0, 1). Find the probability P(X > Y) that X is greater than Y

A: # Here  given that X~U nia,b       fx =1b-a   '   a≤x≤b  0            ' other

Q: E and F are mutually exclusive events. P(E) = 0.1; P(F) = 0.6. Find P(E | F).

A:

Q: Let X be a nonnegative random variable. Prove that. EX (EX) 4E[X*] 2

A: Given that X be a nonnegative random variable. Result: PX≥c≤E(X2)c2               ≥c2EX2

Q: Suppose X, Y are two discrete random variables with probability function given by: Y X-1 1/8 1/8 1/8…

A: Multiplication of marginal probabilities are are compared with joint pmf.

Q: Q1. Suppose that X and Y are jointly continuous random variable - x for 0 < x < 1 and 1 < y < 2 f(x,…

A: As per our company guidelines we are supposed to  answer only first 3 subparts. kindly repost other…

Q: Let f(x) is probability function of discrete random variable x then Σικ) 1 صواب

A: Let, f(x) be the probability density function of district random variable X. we know that the…

Q: Let X be a discrete random variable with probability distributio P(x) = c (1/3) *, x= 0, 1, 2, ..

A: X will consider discrete probability distribution if:

Q: Suppose X and Y are jointly continuous random variables, the conditional expectation of u(x), given…

A: The conditional expectation of u(x) given y is:

Q: Suppose that X and Y are random variables with E(XY) = E(X)E(Y). Then X and Y * independent. Also…

A: We know that if X and Y are independent then E(XY)=E(X)E(Y). But the converse is not always true.…

Q: Let X - Po(A), A > 0. Determine the PMF of the random variable Y = X² – 3 and

A: Poisson distribution: A random variable X is said to have a Poisson distribution with a parameter λ…

Q: If a random variable X is defined such that E[(X-1)*]=10and E[(X-2)²]=6, find ux and o?,

A: Consider           EX-12=10    EX2-2X+1=10EX2-2EX+1=10      EX2-2EX=10-1…

Q: Let X and Y be independent random variables such that with a prob. 1/3 with a prob. 2/3 with a prob.…

A:

Q: 21. Suppose that X and Y are jointly continuous random variable for 0 <x <1 and 1< y < 2 otherwise -…

A: From the given information, Consider, X and Y are jointly continuous random variable with pdf: fx,y…

Q: Let X be a random variable with p.d.f. 2e-2x 0<x<00 f (x) =• , find E(e 2*) O.w

A: Given, the probability distribution function of a random variable X- fx=2e-2x  ; 0&lt;x&lt;∞0…

Q: Q5) Suppose that ƒ(x) = e*for (0< x). Determine the following probabilities: 1) P[1<X] 3) P[X = 3]…

A: Given,f(x)=e-x ; x&gt;0

Q: Let X be a random variable with p.d.f. 3e-3x 0<x<0 f(x) =- find E(e*) O.W

A: As per our guidelines we are suppose to answer first question .

Q: Let X ~ U(a,b). Use the definition of the mean of a continuous random variable to show that μX =…

A: The mean of the uniform continuous random variable can be calculated as:

Q: X and Y are non independent events such that p(X)=0.6 p(Y)=0.7 and p(X u Y)=0.95 Find  a)p(X n Y)…

A:

Q: Let X and Y be continuous random variables with joint p. d. f. f(x, y) = {2 if 0 <y<1-x;0 <x<1…

A: The joint probability density function is fx, y=2 if 0&lt;y&lt;1-x ; 0&lt;x&lt;10, elsewhere

Q: Suppose the p.d.f. of random variable X is defined as x³/20 if1<x< 3 f(x) = otherwise

A:

Q: (a)  You roll two dice: one is blue and the other one is red. Both dice are six-sided with a…

A: S1 1 2 3 4 5 6 S2               1   (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) 2   (2,1) (2,2)…

Q: Let X,Y be non-negative simple random variables. If Y SX a.s., then EY S EX.

A: Let X , Y be non negative simple random variables  If Y&lt;=X as then E(Y) &lt;=E(X)

Q: Let X1 - b(n1, p) and X2 ~ b(n2, p) be independent random variables. a) Find the m.g.f. of Y = X1+…

A: Given that X1 follows b(n1, p) and X2 follows b(n2, p) and they are independent.

Q: Let X be a random variable with p.d.f. 3e-3x f(x) = { 0 <x<00 , find E(x) O.w

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Let V=X+Y and U=X-Y are random variables, then the condition which make the covariance

A: Given that V=X+Y and U=X-Y are random variables. Formula for covariance between U and V is…

Q: Let X - binomial(n, p) and Y ~ binomial(m, p) be independent. a. Derive the MGF of W = X + Y. b. By…

A: 3. Given that X~binomialn,p and Y~binomial(m, p). The MGF of X is, MXt=q+petn The MGF of Y is,…

Q: Let X be a random variable with p.d.f. 2e-2x f(x)=< 0<x<0 , find E(e2") O.w

A: Let  X be a random variable with the pdf  fx=2e-2x                 0&lt;x&lt;∞0…

Q: Let Y1 and Y2 be independent random variables with Y; ~ N (0, 1). 1 Let 1-[":]+c[ %] where C:2 x 2 =…

A: From the given information, Y1 and Y2 are independent random variables with Yi~N0, 1. That is,…

Q: Suppose that X is a random variable for which E(X) = μ and Var(X) = σ2. Show that E[X(X − 1)] = μ(μ…

A:

Q: Let X be a random variable with p.d.f. ((k +4)(x+2) f (x) ={ 0<x<2 , find (1) k (2) E(x) O.W

A: (a) We know, ∫fx dx=1∫02k+4x+2 dx=1∫02kx+2k+4x+8 dx=1kx22+2kx+2x2+8x02=12k+4k+8+16=16k=-23k=-236

Q: Let X and Y be two independent exponential random variables. X ~

A: Given,  X and Y be two independent exponential random variables.                       X~exp(1) and…

Q: Suppose that X and Y are independent random variables with EX=EY=100, and E[min(X,Y)}=79. Find…

A:

Q: Assume that an investor could invest in a risky asset that is expected to earn $150,000 nothing with…

A: The given risky investment can result in two types of returns 150,000 with probability 0.5 And, 0…

Q: for x >1 f(x) = otherwise Given that a randomly selected home is insured for at least 1.5, what is…

A:

Q: Suppose that f(x) = e* for x > 0. Determine the following probabilities:

A: Solution -: Let, X- be the random variable We have,  f(x)=e-x       ; x&gt; 0 We find P[X=3]=?

Q: Suppose (X,Y) is a continuous random variables with joint probability d 4xy Osxs1,0sys1 x,Mx.v) = {"…

A: Let X be a random continuous variable with probability density function(pdf) f(x) then the expected…

Q: - Prove that the moment generating function of the random variable X having the p.d.f. fx (x) =, -1<…

A:

Q: Let be a continuous random variable whose cdf is F(x ). Then P(X=0)=.... ... .A .B 1 .C F(x) .D…

A:

Q: Suppose that X and Y are random variables with E(XY) = E(X)E(Y). Then X and Y * independent. Also…

A: E(XY) = E(X)E(Y)

Q: The probability of the joint event {x, < X ≤ x₂,₁ <Y ≤y₂} is given by P{x <X<x,,y<Y<y,} = Fxy(x,…

A:

Q: Determine the following probabilities: P(X < 0.5, Y < 1.5) and P(X < 0.5) f(x, y) y -2 -1.0 1/3 -0.5…

A:

Q: Let X1 and X2 be continuous random variables with the joint probability - function fx1,x,(x1, x2),…

A: Hello! As you have posted 2 different questions, we are answering the first question (2.2.5). In…

Q: e Prove that E(X) independent. E(X/Y), where X and Y are two random variables which are %3D

A:

Q: Let X be a random variable with p.d.f. 2e-2x 0< x<00 f(x) = , find E(x). O.w

A: We know that, E(x)= integration |x X*f(x) dx

Q: Let X be a random variable with p.d.f. k 1<x<00 f(x) = , find k. O.w

A: According the theorem of probability the sum of all the probabilities is equal to one, that is…

Q: Let X be a random variable with p.d.f. (k 1<x<10 f(x)=- find k. O.W

A: Solution: 11. From the given information, the probability density function of X is

Q: Let x denote the grams of gold obtained in a ton of ore. Consider the two events A = {x|0 ≤ x < 3)…

A: Given that Let x denote the grams of gold obtained in a ton of ore. Consider the two events  A={…

Q: 4.Suppose that X is a random variable for which E(X)=µ and Var(X)=o². Show that E(X(X-1)]=µ(µ-1)+o?

A: It is given that E(X) = μ and Var(X) = σ2