6. The moment generating function of a random variable X M(t) = 0.5 +0.2e + 0.2e³t+ 0.1estThen P(-1.5< X <3.4)=c. 0.9a. 0.4b. 0.7d. e-le. None7. If the random variable X has a chi-square distribution with degrees of freedom r, andif E(SX+3)-33, find var (X)a. 3.46b.12d. 6c. 36e. None

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Please do not give solution in image format thanku 1.Suppose that the moment generating function of a random variable X is MX(t)=exp(2e^t−2) and that of a random variable Y is MY(t)=((4/5)e^t+1/5)^16. If X and Y are independent, find each of the following. (a) P{X+Y=2}= (b) P{XY=0}= (c) E[XY]= (d) E[(X+Y)^2]= ———
The moment generating function of the random variable X is given by mX(s) = e2e^(t)−2 and the moment generating function of the random variable Y is mY (s) =(3/4et +1/4)10. If it is assumed that the random variables X and Y are independent, findthe following:(a) E(XY)(b) E[(X − Y )2](c) Var(2X − 3Y)
Q1- What is the probability that the number of heads and are equal it a lait coin is tossed, a)15 times b)20 times Q2- Suppose the joint pdf of X and Y is given by: F xy (x y)={ ex +3y, if 0<x< 1 and 0<y<1 0 otherwise find E(x) . Q2- Suppose X is a random variable with E(X) = 5 and Var(X) = 2. What is E(X)?
If we let RX(t) = ln MX(t), show that R X(0) = μ and RX(0) = σ2. Also, use these results to find the mean and the variance of a random variable X having the moment-generating function MX(t) = e4(et−1)
Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)
Q4) If X is a continuous random variable having pdf ke~ (2x+3y) x>0y>0 xy) = = e p(x) { 0 otherwise Find a) the constant k b) P(X>1) ¢) X, X2, 02, standard deviation.
9.1) Suppose X1, X2, and X3, denotes a random sample from the exponential distribution with density function shown in the image. a) Which of the above estimators are unbiased for θ? b) Among the unbiased estimators of θ, which has the smallest variance?
Let m(t) be the moment generating function of a random variable X. Show that the random variable W = 10X is m(10t). What is the moment generating function of Z = X-5 in terms of m(t)?
3.) Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)? What is P(X = 0)?
10 Suppose that X is a continuous random variable with pdf given by X(x) =cxα−1e−(x/β)α for x≥0, where α >0,β >0 are some parameters of the distribution, and c is a constant. (a) Find the value of c such that fX is a valid pdf.(b) Find the cdf and the quantile function of X.(c) Ifα= 2 andβ= 4, calculate P(X <1) and find the quartiles of X.
1..Consider that a game involves the spinning of a dial which is not fair. As the dial is not fair, after spinning it is more likely to point in any particular direction than another. Suppose that the movement of a dial, X, can be modelled by the following probabilityfunction f(x) = A sin x; 0 ≤ x ≤ π. (i) Determine the value of A so that f(x) is a pdf (ii) Calculate E(X) and Var(X).
X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2

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6. The moment generating function of a random variable X M (t) = 0.5 +0.2e +0.2e³ +0.1est Then P(-1.5< X<3.4)- a. 0.4 b. 0.7 c. 0.9 If tha and e. None