Let R be the region in R2 bounded by the three lines y=y=1.8, y=xy=x, y=?xy=?x and contains the point (0,0.5). Let (X,Y) be the coordinate of a point chosen uniformly at random on the region RR. Let fXbe the marginal density of the random variable Xthat is a continuous function. Find fX(-0.51). Give your answer in four decimal places.

Answer:

Define a random variable X : [0, 1] -> R on the probability triple ( [0, 1], B[0, 1], Leb ) by X(w) = - logw ifw > 0 and X(w) = 0ifw= 0. Here "log" refers to the natural logarithm. Let fx : (0, 00) - 0, 0o) be the probability density n function of X that is also continuous function. What is fx (2.54)? Give your answer to four decimal places.Let R be the region in R bounded by the three lines y =1.8, y = x, y = -x and contains the point (0, -). Let (X, Y) be the coordinate of a point chosen uniformly at random on the region R. Let fx . be the marginal density of the random variable X that is a continuous function. Find fx (-0.51 ). Give your answer in four decimal places