let & be a random Variable with protaboly land plear) aql se for 821, 2.3. –...
7. Let X be a random variable with distribution function Fx. Let a < b. Consider the following 'truncated' random variable Y: if X < a, if X > b. (a) Find the distribution function of Y in terms of Fx. (It will be a good additional exercise to sketch FY though you don't have to hand it in.) (b) Evaluate the limit lim FY (y) b-00
Exercise 2.3
Exercise 2.3. Student interests. A student is chosen at random. Let A, B, C be the events that the student is an Aeronautics major, a Basketball player, or a Co-op student. The events are not disjoint; we are told P(A) = P(B) = P(C) = 0.38, and P(A n B)-P(A n C) = P( B n C) 0.12, and Find the probability that the student participates in at least one of these three programs, i.e., find P(AUBUC).
Let X be a random variable with PDF fx(X). Let Y be a random variable where Y=2|X|. Find the PDF of Y, fy(y) if X is uniformly distributed in the interval [−1, 2]
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].
Let X be a continuous random variable whose PDF is Let X be a continuous random variable whose PDF is: f(x) = 3x^2 for 0 <x<1 Find P(X<0.4). Use 3 decimal points.
Let X be a random variable satisfying P(-1 X 1) = 0.3, P(X = 1.5) = 0.1, P(1.5 X P(3 X 7.4) 0.3, P(X 10)0.2 2) = 0.2 Find (i) P(X 2 1.3) (ii) P(X 2.3) ii P(1.5< X 2) (iv) P(1.5 3X 38)
Let the random variable X have a uniform distribution on [0,1] and the random variable Y (independent of X) have a uniform distribution on [0,2]. Find P[XY<1].
Let ? be a random variable with a PDF ?(?) = |? − 1| for 0 ≤ ? ≤ ?. Answer the following questions (a) Find ? (b) Find ? (? < 0.5) and ? (|? − 1| > 0.5) (c) Calculate E(?) and V??(?) (?)* Without any computations answer the following questions. Let ? be a random variable with a PDF ?(?) = 1 − |? − 1| for 0 ≤ ? ≤ ? for the same ? as...
Let random variable x be a continiuos random variable and it's p.d.f is given as f(x)=3x^2, 0<x<1 Find the probobility that random variable X exceeds the value of 1/2
Let X be a discrete random variable with PMF: a. Find the value of the constant K b. Find P(1 < X ≤ 3)