Q5(3). Suppose there is random variable X, whose PDF is (10 points, 2 for each): 1x-2)2...
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
2. Suppose that the continuous random variable X has the pdf f(x) = cx3:0 < x < 2 (a) Find the value of the constant c so that this is a valid pdf. (10 pts) (b) Find P(X -1.5) (5 pts) (c) Find the edf of X use the c that you found in (a). (Hint: it should include three parts: x x < 2, and:2 2) (20 pts) 0,0 <
Problem 2 (9 points) Consider a random variable X with pdf given by: (x) 0.06x +0.05 0x <5 4pts P (3.5 < X < 6.5)- Find Find Ex]- 5pts Problem 3 (9 points) Consider a random variable X with pdf given by: f(x) 0.06x +0.05 x -0, 1.5, 2, 4, 5 .ind P(3.5 <X <6.5)- 4pts 5pts Given that EN-3.46, find al
Problem 4: (20 Points) X is a uniform random variable with parameters -5 and 5. Given the event B-VI > 3) 1. (5 points) What is the probability of the event B, P(B)? 2. (5 points) What is the conditional PDF, fxB()7 3. (5 points) Find the conditional expected value, E[X |B]. 4. (5 points) Find the conditional variance, var[X]B].
Problem 3. Suppose that the cumulative distribution function of a random variable X is given by (o if b < 0 | 1/3 ifo<b<1B 2/3 if isb<2 2.9 1 if2 Sb. 3.9 (a) Find P(X S 3/2). (b) Find E(X) and Var(X). 4.10
SHOW ALL WORK ANSWER ALL PARTS Suppose that a random variable X has the following pdf. 2(1-2) 0.5 SX < 1 0 otherwise where p is simply a constant that has yet to be specified (in other words, p isa parameter). For now, we will leave the parameter p an unspecified constant Find P(X>08) Note: your answer will be an expression containing p. Suppose that k>0 is also a constant (not yet specified). Find the expected value of the random...
1. Suppose the random variable as a uniform distribution on [-k,k] a) Construct the pdf X. b) Calculate P(X > 2X > 1) in terms of 'k c) Calculate 'K if P(-2 < X < 2) =
Please answer both. . Suppose that Y is a random variable with distribution function below. 1-e-v/2, 0, y > 0; otherwise F(y) = (a) Find the probability density function (pdf) f(y) of Y. yso (b) E(Y) and Var(Y) 5. Suppose X is a random variable with E(X) 5 and Var(X)-2. What is E(X)?
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
Suppose X is a continuous random variable having pdf (1+x, -1 < x < 0, f(x) = { 1 – x, 0 < x <1, lo, otherwise (a) Find E(X2). (b) Find Var(X2).