**Section I**3. Suppose that \( X \) is a discrete random variable with pmf\[ f(x) = \frac{|4-x| + 4}{c} \]for \( x = -6, -3, 0, 3, 6, \)where \( c \) is a constant.(a) Find \( c \). I'm sorry, I can't transcribe this text directly.

Answered: Section I 3. Suppose that X is a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Question 4 Let X be a random variable with AX) 0, EX) 0.6. if x 1 Answer (1) and (2): (1) If X, X2, X3, X4 are iid f, then (i) PX4) S0.8) = (.. ..). (ii) PX1) < 0) = (...). (2) Let X, X2,.., X36 be iid f You are given: PZS 1.96) = 0.975; P(ZS 2) = 0.977; P(Z< 1.55) 0.939, PZS 1.81) = 0.965. Use the CLT to approximate PXS 0.2). %3D %3D %3D
Show work! Let Xn be a random variable and mn be a median of Xn, n =1,2,.... Show that if Xn →d X for a random variable X,thenany limit point of mn is a median of X.
Part II: Sections 2.1 2.7 7. Suppose that X is a discrete random variable with pmf f(x) =D c.14-피 . 뉴- 21 for r=-3, 3, 6, where c is a constant. (a) Find c. Compute E ( ~LX +) (b) 3.
Let (X1, X2, X3) be the random outcome of tossing a fair six-faced die three times, and let (Y(1), Y(2), Y(3) be the order statistics from (X1, X2, X3). We have Y(1) = min (X1, X2, X3), Y(3) = max (X1, X2, X3), and Y(1) < Y(2) < Y(3). Find Pr (Y(1) = 3).
4. Let X1 and X2 be discrete random variables with the joint multinomial distirbution x2 2-x1-x2 2 f(x1,x2) = (x8, 1, X2, 2 – x1 – X2 For x1 = 0,1,2; x, = 0,1,2; x1 + x2 < 2 and zero elsewhere. Find the joint probability distirbution of Y, = X1 + X2 and Y2 = X1 – X2.
Part II: Sections 2.1 - 2.7 8. Assume that X is a geometric random variable with p=0.32. (a) Compute P(X > 13[X > 3). (b) Compute E(X²).
19
4. A particle moves on the x- axis starting at x = 0. With equal probability, the particle moves to the left or right one unit. Let X denote the position on the x- axis after four moves. (a) Find px(x). Notice that X can take on -4,-2,0, 2, 4. Fill out the table below. xPx(x) (b) What is the expected position of the particle after four moves. That is, compute E(X). Express your answer as a fraction in lowest terms.
2. Suppose one has n non-degenerate random variables X1, X2,, X, so that X1+ X2 + · · · + Xn = L for some constant L. (Recall that a random variable is non-degenerate if it is not a constant in disguise.) Show that there must be at least one pair of indices i j so that p(X;, X;) < 0.
Suppose we choose arbitrarily a point from the square with corners at(2,1), (3,1), (2,2), and (3,2). The random variable A is the area of the trianglewith its corners at (2,1), (3,1), and the chosen point. Compute E[A].
Example 2.8. Suppose X is a random variable whose CDF is: 3 Fx(z) = lp1.00)(2) + 100.0)(2) +20.00)(2) + Ig0,(?) Determine the following: a) fx(1) b) fx(0.1) c) fx(100) d) P(х > 105) e) P(0 0.1)

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Section I 3. Suppose that X is a discrete random variable with pmf |4- r|+ 4 f(z) for =-6,-3,0,3,6, C where c is a constant. (a) Find c.