
For the following distribution: x A Drah Probabilit UNCATTLV OULOOS UUU 10 150 U. DU <...
number? 10 3. Let X be a continuous random variable with a standard normal distribution. a. Verify that P(-2 < X < 2) > 0.75. b. Compute E(지)· 110]
Given a normal distribution with u = 100 and o = 10, c. What is the probability that X < 75 or X>110? The probability that X < 75 or X>110 is .8475.
< 0) = 1/3, and Exercise 9.8. Suppose X has an N(u,02) distribution, P(X P(X < 1) = 2/3. What are the values of u and o?!
(5 pts) Let U be a random variable following a uniform distribution on the interval [0, 1]. Let X=2U + 1 Calculate analytically the variance of X. (HINT : Elg(z)- g(z)f(x)dr, and the pdf. 0 < z < 1 0 o.t.w. f(x) of a uniform distribution is f(x) =
Solve heat equation in a rectangle du = k ( ou + dou), 0<x<t, 0<y< 1, t> 0 u(x, 0, 1) = 0, uy(x,1,1) = 0, with boundary conditions u(O, y,t) = 0, u(r, y, t) = 0, and initial condition u(x, y,0) = (y – į v?) sin(2x).
4. For the distribution f(z; a) = (a +1)xº, 0<x<1, what is the MLE of a based on a random sample X1, X2, ..., Xn?
QUESTION 10 4 If Z is a standard normal random variable, then P(-1.25<= Z <=-0.75) is QUESTION 11 4F It is given that x, the unsupported stem diameter of a sunflower plant, is normally distributed with population mean mu=35 and population standard deviation sigma=3. What is the probability that a sunflower plant will have a basal diameter of more than 40 mm? 4 pc QUESTION 12 A random variable x is normally distributed with u = 100 and o-20, What...
Exercise 4.3.2. Given the BVP-u' =f(x), u(0) = a, u'(1) = b 0 < x < 1. Here the BC's are inhomogeneous. Present the weak formulation of this prob- lem. Hint: Introduce the help function w(x) through u(x)=w(x)+a+bx, where w(0) = 0, w'( 1 ) = 0
1. Let X1, ..., Xn be random sample from a distribution with mean y and variance o2 < 0. Prove that E[S] So, where S denotes sample standard deviation. 10 points
Question No. 6 Suppose that the random variable X has the following uniform distribution: 2 f(x)= 3 ,other wise (18) P(0.33 < X < 0.5) = (A) 0.49 (B) 0.51 (C) 0 (D) 3 (19) P(X> 1.25) = (A) 0 (B) 1 (С) 0.5 (D) 0.33 (20) The variance of X is (A) 0.00926 (B) 0.333 (C) 9 (D) 0.6944