Y is an exponential random variable uith var [y]<25 what i's the PDr of y? what is the ELY]? what is

Q: Let us consider a discrete random variable having the pmf given by, PX(k) = { (1/3) , k = 1   (2/3)…

A: The moment generating function of x is given by: Mxs=EesX=13es+23e2s+0e3sMxs=13es+23e2s

Q: True or False;  For a continuous random variable X, P(X=x) = f(x) 1. True 2.False

A: In statistics, the continuous variables are variables whose values can be given by an interval, they…

Q: Determine if the random process X(t) = A, where A is a random variable with mean A and variance o is…

A:

Q: Let X1, X2, .,X25 be i.i.d. random variables from Po(5). Estimate ... the MSE for the median…

A: A uniform distribution is a probability distribution in which every value between an interval from a…

Q: If X₁, X₂,..., Xn are the values of a random sample from an exponential population, find the maximum…

A:

Q: A random variable X has the following PMF: [refer to image] a) Find E(X) b) If Y = g(X) = X^2,…

A: The PMF of X is given as:

Q: Assume we have a linear model with 2 X variables, X1, X2. Show that the variance inflation factors…

A: variance inflation factor (VIF) : is the ratio  of the variance of estimating some parameter in a…

Q: S Suppose that the time (in hours) required to repair a machine is an exponentially distributed…

A: The distribution of the repairing time for the machine is specified to be distributed exponentially…

Q: U is a uniform (0, 1) random variable and X = −ln(1 − U). Find the PDF, CDF of random variable X.…

A: Here, it is provided that a random variable U has uniform distribution over 0,1. Another random…

Q: Compute the mean of X Variance of X Standard deviation of X

A: The mean of X, E(X) is the first derivative of MGF with respect to t at t = 0 And E(X2) is the…

Q: Suppose that the random variable X satisfies P(X=a) = p and P(X=b) = 1-p, where a<b. Verify that…

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Q: Find the probability of event {X ≤5.5} for a Gaussian random variable having #x Ox=2. = 3 and

A:

Q: 29% of rainstorms are thunderstorms. A climatologist believes this proportion is changing. In a…

A: Solution: Let X be the number of rainstorms were thunderstorms and n be the sample number of…

Q: Let X, and X, be independent exponential distributions with the same parameter 1. What is the joint…

A: Given:  X1 &amp; X2 are independent random variables with pdfs             f(x1)=λe-λx1; x1&gt;0…

Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…

A:

Q: No, this solution is not correct. The variance of an exponentially distributed random variable is…

A: We are given that L is exponentially distributed with a mean of 1/Y, where Y has a gamma…

Q: 2. Let X represents the lifetime of water turbine in years. The lifetime of the turbine is a random…

A: f(x)=ke-0.5x ; x&gt;0

Q: Show that the mean x of a sample of size n from the distribution. e-x/0 f (x)= 0<x< 0 elsewhere is…

A: Here given f(x) which is the distribution of exponential distribution.  We know the mean and…

Q: The random variables x, are i.i.d. and uniform in the interval (-0.5, 0.5). Show that 13 E{(x₁+x2 +…

A: It is given that the random variables X1, X2, X3 are i.i.d and follow Uniform distribution with…

Q: Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ = EX?…

A: Given : X be the random variable  Y=aX

Q: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2…

A: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2 +…

Q: Let Y be random variable normally distributed with mean N =1 and standard deviation 6=2. Use the…

A:

Q: Let X be a random variable such that a. V(3x-3) b. E(3x-3) E(X²) = 58 and V(X) = 40. Compute

A: Answer:- Given, X be a random variable such that  E(X2) = 58 and V(X) = 40               (a) Find…

Q: Derive the MGF for an exponential random variable X ~ exp(A) (try the Kernel trick!) O eta t-入…

A:

Q: If X₁, X2, ..., Xn constitute a random sample of size n from an exponential population, show that X…

A: let X1, X2, ......Xn is an independent identically distributed random variable following an…

Q: A random variable X is exponentially distributed with decay parameter 1/8 . We randomly draw a…

A: Please find the handwritten solution

Q: Suppose random variable X has a Poisson distribution with t​ = 2 and λ= 4. What is​ E(X)?

A:

Q: f(x) = ,2 <x < 5 %3D 39 ,otherwise k to see additional instructions the random variable whose pdf…

A: V[X] = E[X2]- (E[X])2 ----- Formula ________________________________________

Q: Inspection trials are carried out in a factory to assess the quality of products. In each trial r,…

A: Given that  be the number of satisfactory items in the trial and is assumed to follow the binomial…

Q: Derive the mgf of an exponentially distributed random variable with mean β. Verify that(E[Y])2 =…

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Q: Let X and Y be random variables having the same distribution. 1 If X and Y are independent, show…

A: Given that  Let X and Y be random variables having the same distribution.If X and Y are independent,…

Q: (TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.

A: Solution: The covariance between the random variable X and Y can be defined as  Cov(X,Y)= E(XY)-…

Q: Suppose that a random variable X is an Exponential Random Variable with parameter β = 3. (a) What is…

A: Solution: From the given information, X follows an exponential distribution with parameter β=3.

Q: If X1, X2, X, is a random sample from an exponential population having mean 1 find the exact…

A:

Q: Suppose x is a normally distributed for continuous random variable with 4-10 and 6. Find value of xo…

A: First converting the variable into standard normal using z =(x-u)/σ where u is mean and σ is…

Q: Suppose that X ~ Pareto(7). Define Y = In(X+1). If E[X] = }, then what is the variance %3D of Y?

A: The probability density function(pdf) for a random variable X~Pareto(γ) is given by fX(x)=γ(1+x)γ+1,…

Q: Please explain your answer with steps Suppose X and Y are random variables such that E[X] = -3 and…

A: Suppose X and Y are random variables. Given: E(X) = -3 E(Y) = 6 We have to find E(X-Y). E(X-Y) =…

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

A:

Q: Let X be a uniform random variable over the interval 1 to 4 and Y is exponential with a mean of 2.…

A: Correlation Coefficient between two Random Variables: If X and Y be two random variables, then the…

Q: Where does the z=2 come from? Just from X, and Y also being random variables?

A: Solution of the asked question is in step below.

Q: Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).

A: When X~ Pois(λ) P(X=x)=e-λ λx/x!  ; X=0,1,2,3,.. result: r!=r(r-1)(r-2)..3x2x1

Q: Show that the serial correlation coefficient p is equal to -1, if n = 2, provided the denominator is…

A: Solution:

Q: Random variables X and Y are connected through pgf ¤x(s) and Vy(s) by the relation x(s) = s¥y(/s)…

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Q: Suppose that a random variable X has the following moment generating function, Mx (t) = (1-9t)−7, t<…

A:

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!