Compute the following probabilities: P(X+Y > 3) P(XY = 2) = P( > 1) =|
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- The joint probability mass function of XX and YY is given by p(1,1)=0.45p(2,1)=0.05p(3,1)=0.05p(1,2)=0.05p(2,2)=0.1p(3,2)=0.1p(1,3)=0.05p(2,3)=0.05p(3,3)=0.1p(1,1)=0.45p(1,2)=0.05p(1,3)=0.05p(2,1)=0.05p(2,2)=0.1p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.1 Compute the following probabilities:P(X+Y>3)=P(X+Y>3)=P(XY=2)=P(XY=2)=P(XY>1)=P(XY>1)=Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).The number of trams X arriving at the St. Peter's Square tram stop every t minutes has the following probability mass function: p(x) =(0.25t)^x/x! * exp(-0.25t) for x=0,1,2,... the probability that 3 to 5 trams arrive in a 6 minute period is
- The pmf of X is p(0) = .5, p(1) = .3, and p(2) = .2. The pmf of Y is p(0) = .6, p(1) = .1, and p(2) = .3.a) Create a joint probability mass function for X and Y assuming that they are independent.b) Find P(X = 1|Y = 1).c) Find P(Y = 1|X = 1).d) Find P(X ≤ 1 ∩ Y ≤ 1)If X and Y are independent exponential random variables, each having parameter λ.(a) Find the joint density function of U = X + Y by using the convolution of fX and fY .(b) Find the joint density function of V = X − Y by using the method of transformation.(c) Are U and V independent?Suppose that X1, X2, X3 are independent with the common probability mass function: P{Xi = 0} = 0.2, P{Xi =1} = 0.3, P{Xi = 3} = 0.5 i =1, 2,3 a. Plot the probability mass function of X2_average = (X1 + X2)/ 2 b. Determine E [X2_average] and Var [X2_average] c. Plot the probability mass function of X3_average = (X1 + X2 + X3)/ 3 d. Determine E [X3_average] and Var [X3_average]
- If the joint probability density function of two continuous random variables X and Y isgiven byf(x; y) = 2, 0 < y < 3x, 0 < x < 1; find(a) f(yjx),(b) E(Y jx),(c) Var(Y jx).Given the probability mass function of a random variable X p(x) = c/(x+1) if x = 0,1 and p(x) = 0 in other mass points. What is the value of c ?Suppose that the random variables X, Y , and Z have the joint probability density function f(x,y,z)=cxyz for 0 < x < 1, 0 < y < 1, and 0 < z < 1. Find the E(x). Use the Scientific Method of Answering (Given, Required, Formula and Solution.)
- Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.I toss a fair coin twice, and let X be defined as the number of heads I observe. Find the range of X, RX, as well as its probability mass function PX.The Geom(p) probability mass function (pmf) is given byfY (y) = (1 − p)y−1 pfor y ∈ {1, 2, 3, 4, . . . } and fY (y) = 0 elsewhere, Find the P(Y>2) and write the solution in terms of p
