2.5.1. The probability function of a random variable Y is given by where λ is a...
Show work, thanks 2.5.1. The probability function of a random variable Y is given by p (i)-% 1 0, 1, 2, , where λ is a known positive value and c is a constant. (a) Find c. (b) Find P(Y 0) (c) Find P(Y > 2).
The probability mass function of a random variable X is given by Px(n)r n- (a) Find c (Hint: use the relationship that Ση_0 n-e) (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3)
1. The probability mass function of a random variable X is given by Px(n) bv P Yn (a) Find c (Hint: use the relationship that Σο=0 (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3) n-0 n! ex)
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 27 x2 -3x x >0. The kinetic energy of the particle is Y = {mXSuppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.)
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
The random variable X and Y have the following joint probability mass function: P(x,y) 23 0.2 0.1 0.03 0.1 0.27 0 4 0.05 0.15 0.1 a) Determine the marginal pmf for X and Y. b) Find P(X - Y> 2). c) Find P(X S3|Y20) e Determine E(X) and E(Y). f)Are X and Y independent?
Let X be an exponentially distributed random variable with parameter λ. Prove that P(X > s + tK > t) P(X > s) for any S,12 0
[Q#2] (7pts) Suppose a discrete random variable Y has a Geometric probability distribution with probability of success p (>0). Its p.d.f. p(y) is defined as P(Y = y) = p(y) = p (1-p)y-1 for y = 1,2,3, ... Verify that the sum of probabilities when the values of random variable Y are even integers only is 1-p. That is to find p(2) + p(4) +p(6) +.. 2 – p
2.5.9. The random variable X has a cumulative distribution function for xo , for xsO . for r>0 F(x) = z? 1 +x2 Find the probability density function of X.