![Q1. The random variable X has the following CDF 0 Fs(z) = 0.7, 0 z<1 (a) Draw a graph of the CDF (b) Write out the PMF of X. (c) Find out E[] (d) Find out PxIB(z), where B = {Ixl > o). what are EXIB] and VarlX1B)? Q2. Given the random variable in Q1. Let V-g(x)-지. (a) Find the PMF of V. (b) Find Fv(v). (c) Find EV](http://img.homeworklib.com/questions/8975e160-c468-11ea-8215-318888fc09b8.png?x-oss-process=image/resize,w_560)
I only need help on quesiton 2. However, you need 1 to solve 2. Thanks :)
I only need help on quesiton 2. However, you need 1 to solve 2. Thanks :)...
You only need to do Q2 (a)'s (i) and (ii). No need to do part
B
2. (a) Let X be a random variable with a continuous distribution F. (i) Show that the Random Variable Y = F(X) is uniformly distributed over (0,1). (Hint: Al- though F is the distribution of X, regard it simply as a function satisfying certain properties required to make it a CDF ! (ii) Now, given that Y = y, a random variable Z is...
The random variable X has CDF 0 <-1, Ex(x) = 0.2 -1 < 0, 0.7 0 x<1, 1 21. (a) Draw a graph of the CDF (b) Write Px(), the PMF of X. Be sure to write the value of Px(a) for all r from-oo to oo. Given the random variable X in problem ii), let V g X)X. (a) Find P(v). (b) Find Fy(v). (c) Find EIV]
The random variable X has CDF 0 x<-1, 0.2 -1s<O, 0.7 OS<1, 1 21. Fx () (a) Draw a graph of the CDF. (b) Write Px(x), the PMF of X. Be sure to write the value of all a from -oo to oo.
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*
Let X be a random variable with CDF z<0 G()=/2 0 <IS2 z>2 1 Suppose Y = X2 is another random variable, find (a) P(1/2 X 3/2), (b) P(1s X< 2) (c) P(Y X) (d) P(X 2Y). (f) If Z VX, find the CDF of Z. (d) P(X+Y 3/4)
I am studying Continuous Random Variables.
Hope can some one tell me the solutions of these two
problems!
II.1 Let X be a continuous random variable with the density function 1/4 if x E (-2,2) 0 otherwise &Cx)={ Find the probability density function of Z = X density function fx. Find the distribution function Fy (t) and the density function f,(t) of Y=지 (in terms of Fx and fx).
II.1 Let X be a continuous random variable with the density...
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
Let Z ∼ N (0, 1), and let X = max(Z, 0). 1. Find FX in terms of Φ(t). Is X a continuous random variable ? 2. Compute p(X = 0) 3. Compute E(X). Hint: use the CDF expectation formula, and integration by parts. You may assume that limt t nφ(−t) = 0 for all n ≥ 0. 4. Find the CDF FX2 (u) 5. Compute V(X). Hint: use FX2 , and follow the same hint of part (3)
Consider the simplified Bayesian model for normal data The joint posterior pdf is ful, σ21 x)a(σ2,-/2-1 expl_jy.tx, _aPI The marginal posterior pdfs of μ and σ 2 can be obtained by integrating out the other variable (8.30) y@1 x) α (σ2)-m;,-1/2 expl-- Σ.-tri-x)2 (8.31) d. Let q1 and q2 be they/2 and 1-y/2 quantiles of (8.31). Show that the 1-γ credible interval (gi,q2) is identical to the classic confidence interval (5.19) (with ar replaced by y). Hence, a (1-α) stochastic...
4.4.19 Random variableX has PDE fx(a)-1/4 -1s-33, 0 otherwise Define the random variable Y by Y = h(X)X2. (a) Find E[X and VarX (b) Find h(E[X]) and Eh(X) (c) Find ElY and Var[Y .4.6 The cumulative distribution func- tion of random variable V is 0 Fv(v)v5)/144-5<7, v> 7. (a) What are EV) and Var(V)? (b) What is EIV? 4.5.4 Y is an exponential random variable with variance Var(Y) 25. (a) What is the PDF of Y? (b) What is EY...