Let X ~ U(1,3) with the following given PDF (0.5, 1

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Q: Q3/A/ Let X be a r.v with p.d.f f(x) =e-xl - 00 <x < oo, then the value of variance of X is -

A: Given :Let X be a r.v  with p.d.f f(x)=12e-|x|Formula : ∫-∞∞f(x)dx

Q: (3) Derive a general expression for the variance of net future loss Var(L) with a constant force of…

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Q: Suppose that { Y,} is Moving average process with Y, = 0.25(e, + e,-1+e-2+ej_3) %3D where {e,} is…

A: Find Mean, variance, auto covariance function and auto correlation function

Q: (2) The joint p.d.f of the random variables X and Y is e-x-y, x>0, y > 0, { f(x, y)= 0, otherwise.…

A: Given,the joint pdf -..The mean of X, mean of Y, conditional expectation, and conditional variance…

Q: Let (X, Y) be BVN(0,0, 1, 1, p). Find the variance of XY.

A: Given that; (X, Y)~BVN(0, 0, 1, 1, ρ)⇒X~Normal(0,1) and Y~Normal(0,1)Y|X=x~Normal(ρx, 1-ρ2) We know;…

Q: Calculate the correlation coefficient from the following results N-10, ΣX- 350/ Σ Υ- 310 Σ (X-35=…

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Q: Using the theorem, show that the estimator X is a consistent estimator for the parameter p.

A: Given that X1,X2,....,Xn follows Normal distribution.

Q: "What is the correlation coefficient for this condition? X is the voltage across a resistor, Y is…

A: We have given that the statement about to the correlation condition of X and Y.   Note: According to…

Q: There is a linear regression: Yi = B0+ B1(Xi^2)+ ei present, where Xi is squared. ei ∼ N(0,σ2). How…

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Q: The pdf is given as follows: f(x) = { (1/6)e^(1/6x) ; x > 0 0; ew] (i) Find the mean and variance…

A: The pdf is given as follows:f(x) = { (1/6)e^(1/6x) ; x &gt; 0

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A: The MA(3) process is, Yt=ut-0.7ut-1-0.2ut-2+0.4ut-3 Here ut is a white noise process with variance…

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Q: Show that the conditional variance can be written as σ^2 (X) = E { Y^2 | X} −(E[Y | X])^2     no…

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Q: a JPDF f(x,y) = 8/81 xy for 0<x<3 and 0<y<x. Let V(X) = 5.76 and V(Y) = 2.56 Find the correlation…

A: Solution:f(x,y) = 818​  where, 0 &lt; y &lt; x  &amp; 0 &lt; x &lt; 3 So,E[xy] =…

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Q: (i) Compute the KL-divergence of Normal RV with (mean) parameter µ1, µ2 under prob- ability measure…

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Q: Let E(X|Y = y) = 3y and var(X|Y = y) = 2, and let Y have the p. d.f. if y > 0 f(G) = {o otherwise…

A: Given, EX|Y=y = 3y and varX|Y=y=2 The pdf of Y as follows: fy=e-yif y&gt;00otherwise

Q: Suppose W = (aX + 3Y) 2 where Y, X are two random variables with zero mean and variances 20x = 4,…

A: As, X~N(0,4) and Y~N(0,16) E[x] = 0 Var[x] = 4 E(x)2 - [E(x)]2 = 4 E(x)2 - 0 = 4 E(x)2 = 4 Now, E[y]…

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Q: If 1. If for >0 the energy of a pdf is E(x)=r, find the variance. (A) 1 (B) 2 (C) 1/2 (D) Undefined…

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Q: Suppose that a random man's weight from a certain population is M Normal (u 200, o²49) and a random…

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Q: There is a relationship between the following variables as y = 1 / (a ​​* x ^ b) (x ^ b: means x…

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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!