Consider the following pdf: ; 0<x<1 f(x)-2k ; l<x<2 0 otherwise (i)Determine the value of k. (ii) Find P(X 0.3) (iii) Find (0.1 〈 X 1.5).
Given that 0<x< 2π, solve the followi ing inequalities. (2) 2sin2x <3cosx (3) 2cosx3 sinx+10
1. For pdf f (r, y) = 1.22, 0 < x < 1,0 < y < 2, z +y > 1, calculate: EY) and () E (X2)
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?
Suppose that f (x II 2y), 0 < x < 1,0 < y < 1. Find EX + Y).
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
The size (in mm) of a crack in a structural weld is given as: X 0 < x < 2 011-12 f(x)= 2 < x < 5 4 otherwise so i. What is the probability that a crack will be smaller than 4 mm? Find the mean crack size. iii. Suppose there are four cracks in the weld. What is the probability that only one of these four crack size is larger than 4mm?
Solve the inequality f(x) <0, where f(x) = - x2(x + 4), by using the graph of the The solution set for f(x) <0 is. (Type your answer in interval notation.) function. Ay 4- 2- х 500 -8 -6 -4 -2 2 4. 6 -8- -104 -12-
Find all values on the graph of f(x) = x + 2 sin x for 0 < 3 < 2 where the tangent line has slope 0.
Problem 3: X and Y are jointly continuous with joint pdf 0<x<2, 0<y<x+1 f(x,y) = 17 0, Elsewhere a) Find P(X < 1, Y < 2). b) Find marginal pdf's of X. c) f(x|y=1). d) Find E(XY). dulrahim