5. If a, b E R, prove that abl < (a + b^).
Prove that A = B for: A = {(x,y) e Rº : +y/<1} B = {(z,y) € RP: (71+ y)² < 1}
The following ψ are m.gf of some random variable X. Find EN] and Var(X) in each case. (a) ψ(t) = e2(e-1),-oo < t < oo.
1. Find the complex Fourier series of the following f(x) = x, -π < x < π
Question 20 Find a theta notation for the number of times the statement x = x + 1 is executed: 12 while i<n) 12 - - 1 02") (1) e(n) edign) On ign) edgign)
Discrete Math in the final answer) 6. Write the negation of the following statements (without using (a). Un e Z+, 3p EP, n3 <p < (n + 1)3. (b). Vce R+,3K EZ+, Vn e Z, n > K → n n+100 < c.
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
Let X be a geometric random variable with p = 0.83. Use your calculator to find PX < 4)
2. Suppose X and Y have the joint pdf fxy(x, y) = e-(x+y), 0 < x < 00, 0 < y < 0o, zero elsewhere. (a) Find the pdf of Z = X+Y. (b) Find the moment generating function of Z.
The random variable X has the probability density function (x)a +br20 otherwise If E(X) 0.6, find (a) P(X <름) (b) Var(x)