3.22 The p.d.f of the random variable Xis given by f(x) = c\sqrtx for 0<x<4, and 0 elsewhere. Find the value of c and P(X<1\4) and P(X>1)
3.22 The p.d.f of the random variable Xis given by f(x) = c\sqrtx for 0<x<4, and...
Let random variable x be a continiuos random variable and it's p.d.f is given as f(x)=3x^2, 0<x<1 Find the probobility that random variable X exceeds the value of 1/2
The random variable x has a p.d.f. given by: f(zfor 0 2 Find the UPPER quartile, Q3 O 0.5 O 0.375 0.75 1.5 Given the following joint probability distribution of X and Y 10.0450.08l10.1 Then X + Y takes on values 2,3,4,5, and 6. Build the probability distribution for Z = X + Y by matching the appropriate probability to each value of Z. 1. 0.16 2. 0.215 3. 0.27 4. 0.045 5. 0.315
1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for 0 〈 x 〈 2. r for 0<< f(x) = 0 otherwise. Let Y - X (2 - X). First determine the c.d.f. of Y, then find its p.d.f. (Hint: when computing c.d.f., plotting the function Y- X(2 - X) which may help. )
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).
7.77. If X1, X2,.., X, is a random sample from a distribution with p.d.f. f(x;0)=0*xe-, 0 <x< 00, zero elsewhere, where 0 e< ao: (a) Find the m.l.e., 6. of 0. Is 6 unbiased? X and then compute E(0). Hint: First find the p.d.f. of Y = (b) Argue that Y is a complete sufficient statistic for 8. (c) Find the unbiased minimum variance estimator of 0. (d) Show that X/Y and Y are (e) What is the distribution of...
4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x > 0, and mean θ. A single observation of an exponential random variable X is used to test H0 : θ-2 against H1 : θ-5. The null hypothesis is accepted if and only if the observed value of the random variable is less than 3. (a) What is the probability of committing a Type I error? (b) What is the probability of committing a Type...
The distribution function of a random variable X is given by 0 Fw={ F(2) = 1+2 <-1 -1<r<1 => 1 "iszai (a) (5 points) Find the p.d.f(f(x)) of X (b) (5 points) Find P(0.3 < X <0.5)
OUESTION 3 (20 MARKS) Consider the following joint p.d.f. oft random variable X and Y. f(x,y)= kaz’ye", 2>0, 0 <ysi 0, elsewhere (1) Determine the value of the constant k. (6 Marks) Computer E (2'y) (6 Marks) Determine E (z'ly). What can you say about the two random variables? (8 Marks)
Let X be a random variable with p.d.f. f(x) = θx^(θ−1) , for 0 < x < 1. Let X1, ..., Xn denote a random sample of size n from this distribution. (a) Find E(X) [2] (b) Find the method of moment estimator of θ [2] (c) Find the maximum likelihood estimator of θ [3] (d) Use the following set of observations to obtain estimates of the method of moment and maximum likelihood estimators of θ. [1 each] 0.0256, 0.3051,...
2. Suppose that the p.d.f. of a random variable X is given as in last question. Now let Y 4-X3 Find its p.d.f