9. The random variable X' is said to be obtained from the random variable point a if by truncation at the | Χ(ω) x'(@) = if X (@) < a, a if X (@) > a. Express the distribution function of X' in terms of the distribution function of X.

Q: Let the random variable X have the pdf f(x) = e-ª for 0 < x < ∞, and 0 elsewhere. Compute the…

A:

Q: The distribution of the random variable X is determined by the function: f(x) = ((x-1)2)/c ; for…

A:

Q: let k be a random variable that takes with equal prob 1/(2n+1), the values in integer the interval…

A: Let X be a random variable that takes on integer values in the interval [-n, n] with equal…

Q: The moment generating function of the random variable X is given by mX(s) = e2e^(t)−2 and the moment…

A: Given that both random variables X and Y are are independent. The mgf of X is:MX(t)=e2et-2By using…

Q: Suppose that a continuous random variable X follows a uniform distribution over {-4, 4]. (a) Find…

A:

Q: X is known to follow the Beta distribution with the parameter 0 = 1000, a = 2, b = 1. wwwww Define…

A:

Q: 7. Let (r1, 12, ., T„) be a random sample from a normal distribution with mean u and a variance o?.…

A:

Q: X is a normally normally distributed variable with mean µ = 30 and standard deviation o = 4. Find a)…

A:

Q: Let X have PMF P(X = k) = −p^k/(k log(1 − p)) for k = 1, 2, 3, ...,where p is a parameter such that…

A: Let X be a random variable. The expected value of X or the mean of X, denoted by E(X) or μX​ is…

Q: Let X be a continuous random variable whose moment generating function is 4x(t) = (³.) ³. Find Var…

A:

Q: Let X be a random variable such that E(X) = 3 and E(X') = 13. Use Chebychev's inequality to…

A:

Q: Let rt be a log return. Suppose that r0, r1, . . . are i.i.d. N(0, 0.01^2). (a) What is the…

A: we have given - rt be a log return. Suppose that r0, r1 . . . are i.i.d. N(0, 0.0001). a) since ,…

Q: then the value of variance of X is

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q2\\ let X be a continuous random variable with pdf: 0 <x <1 1 < x < 2 Sa(x) = {} otherwise Find the…

A:

Q: Q4) If X is a continuous random variable having pdf ke~ (2x+3y) x>0y>0 xy) = = e p(x) { 0 otherwise…

A: Given data: To find:

Q: Suppose X₁, X2,..., X₁ are i.i.d. exponential random variables with pdf given by fx(x) = [e-Az if x…

A: It is given that  are i.i.d. exponential random variables with pdf given as:

Q: Ex//let xa random variable with pm f p X=xN N , x=1,2,.., N and let Y=a+bx where a, bER find Ey and…

A:

Q: Verify that this is the variance of a constrained maximum likelihood estimator VAR[BMCR] = VAR[B] –…

A:

Q: 12. Let a random variable X has a geometric distribution with p.d.f. f(x) = pq*", k =1,2,3,. Show…

A:

Q: Suppose that X is a continuous unknown all of whose values are between -3 and 3 and whose PDF,…

A: Find the constant c: The value of the constant c is obtained as 1/36 from the calculation given…

Q: 3 Let Y~ N (4; o?1,) with and o = 3. Y'Y (a) What is the distribution of o2 (b) Calculate the mean…

A: In

Q: Let X1, X2,..., Xn be a random sample from a distribution with a pdf ke-ka, x > 0 f (x) = 0,…

A:

Q: 20. A continuous random variable X has CDF given by if x <1 F(x) ={2(x – 2 + 1/x) if 1<x<2 if 2 < x…

A: As Prof. A. K. Giri defined, "Probability Density Function: A continuous function f(x) is said to be…

Q: 3. The length of time required by students to complete a 1 hour exam is a random variable with a pdf…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: 17. Let (y1, Y2, ..., Yn) be a random sample from a normal distribution such that E(y;) = a + Bxi,…

A:

Q: Let X be a continuous random variable with PDF 2e*,0 3).

A:

Q: Let X~ N(0, 1) and let Y = -X. (a) Show that Y~ N(0, 1) (by showing that Y has cdf Þ). (b) What is…

A: X follows a standard normal distribution.

Q: Let X1, ..., Xn be independent random variables with the distribution from the first problem…

A: Given that be independent continuous random variables.

Q: =. Let X, Y and Z have the joint pdf x² + y? + z x2 + y? + z2 (2т) 3/2 1+ xyz exp exp where -o < x <…

A: The joint density pdf of X, Y and Z is, fx,y,z=12π32e-x2+y2+z221+xyze-x2+y2+z22 Consider,…

Q: Let X1, X2, . .., Xn be a random sample from a population with a pdf a+2022 (a+ 2021) () ; х > 0, а…

A:

Q: 5. Suppose that X~U(a, b), where U represents a continuous uniform distribution; that is, the pdf of…

A: X is continuous uniform distribution in the interval (a,b). X ~ U(a,b) So, Variance of X, Var(X) =…

Q: Suppose the inter-arrival time of people using the elevator can be modeled as X ~ Exp(1/6) (in…

A: From the given information, It has been given that X is the random variable that shows inter-arrival…

Q: Let X1, X2, ..., Xn be a random sample having the common pdf f(xr, 0) = exp[-(x – 0)] for r2 0. (i)…

A:

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: For an exponential random variable (X) having θ = 4 and pdf given by: f(x) = (1/θ)e^(−x/θ ) where x…

A: We want to find the mean and variance and P(X&gt;3)= ?

Q: Suppose that two random variables X and Y have the joint PDFfXY(u, v) = {60(u^2)v…

A: Step 1:Step 2:Step 3:

Q: 0, x)

A: a) The required value is calculated as follows: fx=ddxFx      =ddxx24     =2x4     =x2…

Q: If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?

A: is a continuous random variable following a uniform distribution, that is .

Q: Suppose Y1,Y2,··· ,Yn are i.i.d. continuous uniform(0,1) distributed. (a) Prove that the kth-order…

A: Given that the iid continuous random variables Y1, Y2, . . ., Yn follow Uniform0,1 distribution.

Q: find k.

A: Given a probability density function, we need to find value of k.

Q: Q6. (a) Let X; (i = 1, ..,n) be independent random varables E(X;) = u and var(X;) = of (i = 1, .,n).…

A:

Q: et X(1) 0. a) Show that X and X) - X() are independent for any s>r. p) Find the distribution of…

A:

Q: a) You throw two fair dice labeled 1, . . . , 6 independently of each other and let X be the minimum…

A: a) The possible out comes of rolling a pair of die are, Let 'x' be the minimum of the ordered pair.…

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!