Let X has uniform distribution on [-1,1]. Find E(X|X²).

Q: Let X and Y be independent v.a with uniform distribution on the interval (0, 20) and (0, 30)…

A:

Q: Let X have an exponential distribution with parameter > 0. Find p P[k < X < k +1] = p(1 − p)k . such…

A:

Q: Suppose that the random variable X has the probability density function ´c(1- x²) for - 1< x s1 f(x)…

A: Given that  Probability density functions of X is  f(x)= c(1-x2)   , -1&lt;=X&lt;=1       = 0…

Q: Let X be a continuous random variable with PDF x> 0 fx(x) ={0 0. otherwise Find E[X], Var[X] and…

A: Simple integration

Q: Determine k so thatf(x, y) = kx(x − y) for 0 &lt; x &lt; 1, −x &lt; y &lt; x0 elsewherecan serve as…

A:

Q: Let 1 1 f(x) = Ix-31, 1≤x≤ 5. 4 Deduce that the function above is a probability density function of…

A: Solution

Q: (x, if 0<x < 1, 2-x, if 1 s x < 2,, (0, elsewhere Let f(x) find the distribution function F.

A: We have to do integration interval wise.

Q: Let X be a continuous random variable with a pdf f(x) = { kx5     0≤x≤1,             0…

A:

Q: 5. If F (x) = P[X < x] is continuous in x, show that Y = F(X) is measurable and that Y has a uniform…

A: The following solution is given below :

Q: Prove that the rv Y=(tan^-1(X1/X2)) and Z=(X1^2+X2^2)^0.5 are independent.   No distribution is…

A:

Q: f the random variable X follows the uniform distribution U= (0,1) What is the distribution of the…

A:

Q: Let X1,X2,,X„ be a random sample from a distribution with pdf 1 f(x;0)= T2 fr-0)}12,-00<x<o,-0 <…

A: From the given information, fx,θ=12πe-x-θ22, -∞&lt;x&lt;∞, -∞&lt;θ&lt;∞ Given hypothesis:…

Q: Let X be a continuous random variable with pdf 0 <x <1 1<x < 2 2 < x < 3 ax a f(x) = -ax + 3a…

A: (i) As if f(x) is a pdf then ∫-∞∞f(x)dx = 1⇒ ∫01axdx + ∫12adx + ∫23(-ax + 3a)dx = 1⇒ ax2201 + ax12 +…

Q: Let X have the Poisson distribution with parameter Y, where Y ha he Poisson distribution with…

A: It is given that,  Y~PoissonμX|Y~PoissonY   We know that if Z~Poissonλ Then,  EetZ=eλet-1

Q: Let F be a distribution function on the line with only two discontinuities at 1.2 and -1.4 with…

A: From the given information, Consider, F be a distribution function on the line and it has been…

Q: Assume that X follows a continuous uniform distribution on the interval [3, 8]. Find P[X s 6].

A:

Q: Let X be a continuous random variable with pdf f(x). If f(x) = 0 for x 0, P(X >a) < a where μ-…

A: Continuous Random Variable: A continuous random variable is a variable whose value can be obtained…

Q: 3. If X has a uniform distribution in (0,1) with p.d.f f(x)=1, 0<x<1 = 0, otherwise. Find the…

A:

Q: Determine the value of k such that the function f(x y)= 4kxy for 0<x<1.5 and 0<y<1.5 satisfies the…

A:

Q: Let X and Y be continuous random variables with joint distribution function,   F (x,y).  Let g…

A:

Q: Let X be uniformly distributed over (0,4). Calculate E[X5].

A: Given: X follows Uniform distribution over ( 0 , 4)

Q: Let X be a random variable with pdf f(x) = 3(1 – x)² when 0 <æ < 1, and f(x) = 0 otherwise a. Verify…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let X be the random variable having pdf f(x) = 1,0 < x < 1, zero e.w. Compute the probability of the…

A: Give X~U(0,1)  P(X(4)-X(1)&lt;1/2)= ?

Q: Find the values of constants 'a' and b' such that Fx (x) = [1-a ·e*/b] u (x) is a valid distribution…

A:

Q: Let X be a continuous random variable with density functionf(x) = 3x^-4, x ≥ 1. Compute E(X ) and…

A: Given function is, fx=3x-4, x≥1 Now, Ex is computed as follows:…

Q: Let X be a continuous random variable with E(X)=i! for i=0,1,2,.... (a) Show that X has an…

A: Yes it is a Gamma distribution with parameters (1,1)

Q: Let X be a continuous random variable with PDFfx(x)= 8/x3, x> 2. Find E[W where W = X/3.

A:

Q: Verify that the following is a distribution function: X a

A:

Q: Let (3x2, 0< < 1 p(x) = otherwise Show that p(x) is a probability density function. Compute its…

A: Given:p(x)=3x2,0≤x≤10otherwise

Q: Var (Y) = E (Y2) - E (Y)2

A: Given that y be a continuous randomvariableThen, we know

Q: Let X(1) 0. a) Show that X4) and X(6) – X() are independent for any s>r. b) Find the distribution of…

A:

Q: IfX is a RV with a continuous dištribution function F(x), prove that Y = F(X) has a uniform…

A:

Q: Let X have a gamma distribution (a, ß)and Let Y = ex.Find G(y)and g(y) by D F method %3D

A: From the given information, X be a gamma distribution α,β. The pdf for X is, f(x)=βαΓ(α)xα-1e-βx The…

Q: The pdf of x is defined as: K f(x)= - A<xS A |2E – Kx² Where, E is the parameter and K is the…

A: Cumulative Distribution Function  is the probability of occurrence of various events together within…

Q: Let x be a continuous random variable that can take any value in the interval [0,3]. Let its…

A: Solution:

Q: Let X be a continuous random variable with PDF, |ax? fx(x) = :0<x<2. 0 : otherwise

A: Consider X be a continuous random variable. Then a continuous function f(x) is said to be a…

Q: Let X be a continuous random variable with the following PDF fx(x) = - 0, x 20 x< 0 where c is a…

A: Given: fxx=ce-x,x≥00,       x&lt;0

Q: Let X have a uniform distribution on the interval [A, B]. (a) Obtain an expression for the (100p)th…

A: Given that, Let X have a uniform distribution on the interval [A, B].

Q: Show that the standard normal probability density function f(x) has points of inflection when x =…

A: Concept - Inflection point is obtained at f''(x) = 0.Given function f(x) - f(x) =…

Q: 3) Let X be a continuous random variable with PDF 1 x20 fx(x) ={0 otherwise Find E[X], Var[X] and…

A: Let X be the continuous random variable with pdf, fX(x)={1θe-xθ; x≥00; otherwise To find E[x],…

Q: Assume that X1, X2, X3 ∼ Exp (λ) are independent and evenly distributed with the distribution Exp (λ…

A:

Q: Let X be a random variable with density function: [K(1=x³) f(x) = { 01 if 0sxs1 otherwise The value…

A: The total probability is always 1. So, ∫-∞∞f(x)dx=1

Q: Show that the function f(t) = -,te Z 21 %3D 5SIS 10, defines a discrete probability distribution by…

A:

Q: 1. If X is a continuous RV having distribution function F(x) (i) Find the PDF f(x), (ii) Find P {X >…

A: Given Cdf  F(X)=1-e-2x if x≥0

Q: Let X be a continuous random variable with probability density function kx2 0 < x < 1 k(2 – x) 1 < x…

A: We know that probability density function is equal to 1.

Q: Let X be a random variable on a closed and bounded interval [a, b]. Let g(x) be a convex function.…

A: Given that g(x) is a convex function. Use the definition of convex function, to determine g(x). From…

Q: Find the m.g.f. for triangular distribution defined by f(x) = x₁ f(x) = 2-x. 0≤x≤ 1, 1 ≤ x ≤2.

A:

Q: Consider a Uniform distribution defined as fx(x) = 36 2<x <8, %3D еe. w. 1. Find E (). O 0.462 О…

A:

Q: Let X be a continuous random variable with the following PDF: 2x fx(x) = 0 < x <1 otherwise Let also…

A: The concept of cumulative distribution functions (CDFs). The CDF for continuous random variables can…

Q: The pdf of x is defined as: 1 f(x)= K - A<x< A n V 2E – Kx Where, K and E are the parameters. 1)…

A: Cumulative Distribution Function is the probability that shows the overall chance of occurrence of…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!