If u (E) =0, then E is measurable.

Q: (a) Show that y for the given z = e" In x+ xy

A:

Q: Suppose f(x) is pdf and is the mean of the random variable, then |(x – 4° f (x) dx = / x²f (x) dx –…

A:

Q: Suppose that Y ~ Normal(0, 1). Compute E[Y³].

A: Solution

Q: The Weber-Fechner law states that if Y is the physical intensity of sound and X is the perceived…

A: From the given information, fY(y)=ye-y22, y>0 And X=klog(Y)Xk=logYeXk=Yexk*1k=dydx

Q: Prove that for a continuous random variable X,E (aX+ b) = aE (X) + b.

A:

Q: A large but sparsely populated county has two small hospitals, one at the south end of the county…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Q: 2. Let X be continous with pdf f(x) = 1/x² if 1 < x < ∞, and 0 otherwise. (a) Does E(X) exist? (b)…

A:

Q: Let X1,..., X, be independent such that X;|p ~ Bernoulli(p) with pE (0,1), and p~ Uniform(0, 1).…

A: c) Given that X1,X2,.....,Xn be independent such that Xi|p~Bernoulli (p). f(Xi|p)=pxi(1-p)1-xi…

Q: Let X and Y have the following joint distribution: X \Y          0          1    0          0.40…

A:

Q: Prove that if 'X' and ʼY' are 'random variables taking real values then [E(XY)}]SE[X°] • E[Y²].

A:

Q: Suppose we have the quadratic function f(x)=A(x^2)+C where the random variables A and C have…

A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

Q: Give the value of c in the interval [0,2] that satisfies the conclusion of the mean value theorem…

A: We have been given a function g(x) = 4sqrt(x)-3 and we need to find the value of c on the interval…

Q: If T(x)be an estimator of 0, then bias term can be defined as, 0- E[T(x)] E[T(x)]=® E[T(x)]-®² a) b)…

A: Solution: Unbiased estimator: A statistic T(x) is said to be an unbiased estimator of θ if E [T(x)]…

Q: Suppose we have the quadratic function f(x)=A(x^2)+2X+C where the random variables A and C have…

A: Let the quadratic equation is f(x)=Ax2+2X+C. From the question, f(A)=A2     0≤A≤2 f(C)=3C2    0≤C≤1…

Q: Suppose X is a continuous random variable with proposed pdf f(x)=cx for 0<x<2 a) Determine the value…

A:

Q: If a is uniformly distributed over [-18, 30], what is the probability that the roots of the equation…

A:

Q: Prove the following: (a) E (C X) = Č E(X) (b) E (X + Y) = E(X) + E(Y) (c) E (XY) = E(X) · E(Y) When…

A: Answer: For the given data,

Q: Let x~ exp (A) Show that T=s Xi is sufficiency Statistic.

A: Generally we use factorization theorem to obtain the sufficient statistic.

Q: Let X be a geometric with success parameter p and pdf P(X = x) = (1 –- p)*-'p x= 1,2, 3, ... 0<p< 1…

A: Consider the given pdf, PX=x=1-px-1p Consider that the mean of a geometric probability distribution…

Q: (b) Determine e so that п п c£[(x; - X;)² i=l j=1 is an unbiased estimator of o². s2 ogunl to

A: 6. From the given information, X1,.....,Xn~f be an iid random sample with mean μ and variance σ2. a)…

Q: Is 1 ;s= 0,1,2,.… P(S = s) = fs(s) = {1+ 1[1 + 1 %3D %3D 0; e.w. a discrete probability function?…

A: For the discrete probability function ,  ∫-∞∞f(x)dx=1…

Q: Let X1, ·.. , X, " f (x;0) = e-=/°, x > 0. (i) Find the sCore and information functions of 0. (i)…

A:

Q: A certain brand of upright freezer is available in three different rated capacities: 16ft3, 18 ft3,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: If f(x) = e-;0 < a < oo denotes the %3D pdf of a continuous random variable X, then find P(-1 < X <…

A:

Q: E (x. - x Y Show that is a consistent estimator for o is N (µ, o²).

A: ANSWER: For the given data,

Q: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý -ye

A:

Q: Is 1 s = 0,1,2,…. ... P(S = s) = fs(s) = {1+1[1 + 1 %3D %3D 0; e.w. a discrete probability function?…

A: Since the domain (s) is defined pointwise rather than as an interval

Q: Find the value of c which satisfies the Mean Value Theorem with the given / (x) =e", [0, 1]. A Inx…

A: Given, f(x)= ex [0,1] b=1 a=0

Q: An M.V.U. is unique in the sense that if T, 1 M.V.U. estimators for y (0), then T, = T, almost

A: A sample statistics t is said to be unbiased estimator of population parameterγ(θ) if expected value…

Q: Verify the following statistical identities: a) E (T; – T)² = E1 x} – nữ² b) E1(C; – T)(y: – 9) =…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: In the U.S., for fellowship, the Casualty Actuarial Society requires passing a series of nine…

A: Given, p1=probability for a student to pass exam 1 pi=probability for a student to pass exam i, if…

Q: Theorem 3-14. For a fixed B with P( B) > 0, P (A \ B) is probability function.

A:

Q: If X is a continuous random variable and y = aX + b Prove that E ( Y ) = a E ( X ) + b and V (Y) =…

A:

Q: H/W: if X and Y are continuous random variables, prove E[X] = E[E[X|Y]]? %3D

A:

Q: (a) Let X be a random variable and c is an arbitrary constant. Determine the value of c which makes…

A: Dear students as per guidelines we answer the first question only when multiple different question…

Q: Let X₁ and X₂ be the payoffs of two investments with E(X₁) = E(X₂) = 10. The expectation of the…

A: Given, X1 and X2 be the payoffs of two investments with EX1=EX2=10.

Q: Show that if t" = (t+t) where t and ť are both most efficient estimators with variance v, then var…

A:

Q: This result leads immediately to an important generalization. Consider a function of X and Y in the…

A:

Q: Let Xi. ---- Xnd Glle e) and Tet TX = Exi , a) show tha T) is unbiased estimator for WcO) =nG: E…

A:

Q: 2. For the following discrete variable with probability f(x) X 2 3 4 f(x) 0.2 0.15 2c 0.05 0.1 (a)…

A: Given:

Q: 2. For the following discrete variable with probability f(x) X 1 3 4 5 f(x) 0.2 0.15 2c 0.05 0.15…

A: Given:

Q: 5. If X-Beta(a, ß) show that E(X) = and Var(X) : aß (a+B)=(a+B+1) a+B

A: We have to show that X follows beta distribution then find expectation and variance of x with alpha…

Q: Let X be a positive random varia (a) E(1/X) > 1/E(X) (b) E(-log(X)) >-log(E(X)) (c) E(log(1/X)) >…

A: Jenson's inequality states that if h is continuous and convex function on interval I and X is a…

Q: Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+1

A: Solution

Q: Let X be a positive random variable (i.e. P(X 1/E(X) (b) E(-log(X)) > -log(E(X)) (c) E(log(1/X)) >…

A: Expectation of a Discrete Random Variable: The expectation of a discrete random variable X, denoted…

Q: What is the value of In(e*)

A:

Q: For random variables X and Y such that E(X) = 2, E(Y) = 1, E(X²) = 10, E(Y²) = 3, and E (XY) %3D с,…

A:

Q: Prove that by Gamma Function pit +e e-st dt %3D s2 +1

A: Gamma Function: The gamma function, denoted by is denoted by which is convergent for Some…

Q: If X has the exponential distribution given by: f(x) = 4*(1 - x/2); 1 ≤ x ≤ 2.   Find E(x).

A: Solution: From the given information,

Q: e: ZN ZP

A: Given: MN¯≅MP¯, NO¯≅PO¯ To prove: ∠N≅∠P

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.