Let X Geometric (0.9).(₁Write down the first five values of the probability mass function of X. (This has asimple answer in decimal form.)Px(1) Px(2)Px(3) Px(4)Px (3)Px (5).) Find the conditional probability mass function of X | A, where A is the event "X ≤ 5".(This has a simple answer in fractional form.)Find E[X|X<5).PxA(1) PxA(2) PxA(3) PxA(4) | PX|A(5)1(3).

The probability mass function (PMF) of a geometric distribution with parameter p is given by:…

Answered: Let X~ Geometric (0.9). (₁ Write down…

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

Suppose that you start with an initial fortune of 20 dollars, and you bet one dollar each time. The probability of winning each hand is p. You quit if you reach your goal of L dollars or when you go broke. Let Q(xo) denote that probability that you eventually win. We need to characterize this probability. Next we give a more mathematical description of the problem. Now define your fortune at time n ≥ 1 by - Xn = Xn-1+ I{Y=1} = I{Yn=0} with the initial condition X = x0 ≥0. Let L = N be given, and define T inf{k : Xk = 0 or Xk = L}. Finally, let Q(x0) = P{XT = . L}. Show that X is a Markov chain and obtain its transition probability matrix. Is it irreducible? Use conditional expectations to prove that Q(x)=pQ(x+1) + (1 − p)Q(x − 1), - x = 1, L-1, (1) with Q(0) 0 and Q(L) = 1. = d) Solve the difference equation in (1) analytically. Let P(x0) P{XT = 0}. Determine P(x) directly and show that P(x) + Q(x) = 1. Hint: Use the same form of the difference equation and analytical solution as in…
Consider the following function for a value of k.f(x) ={3kx/7, 0 ≤ x ≤ 1 3k(5 − x)/7 , 1 ≤ x ≤ 30, otherwise.Comment on the output of these probabilities below, what will be theconclusion of your output.(i)Evaluate k.(ii)find (a) p(1 ≤ x ≤ 2) (b) p(x > 2). (u) p(x ≤ 8/3).
A college finds that 10% of students have taken a distance learning class and that 40% of students are part time students. Of the part time students, 20% have taken a distance learning class. Let D = the event that a student has taken a distance learning class and E = the event that a student is a part time student. For each part, show how you derive your answer. Show formulas if appropriate. (a) Find P(D and E) (b) Find P(D or E)
When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 5 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)equals=0.00762,where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W) denote, and what is its value? What does P(W) represent? P(W)=
A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. If X is the number of defective sets purchased by the hotel, (a) find the probability distribution of X, express it in a table format. Probability distribution of X X P(X) (b) Find the cdf of X. (c) Find the E(X) and Var(X)
Suppose X-U (-54, 60) and F(t) is the cumulative distribution function. What is the probability that X is in the interval [-51, -21] or in the interval [-36, 57]? O (F(-21)-F(-51))+ (F(57) - F(-36)) O (F(-21)-F(-51)) x (F(57) - F(-36)) O F(-21)-F(-36) O F(57) - F(-51)
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?
The circuit shown below operates if and only if there is some path of functional devices from left to right. The probability that each device functions is shown for each device and the devices operate independently of each other. What is the probability that the circuit operates? 0.9 0.9 0.8 0.95 0.95 0.9 (A) None of these (B) 0.5263 (C) 0.1642 (D) 0.9850 (E) 0.9702
Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?
Two real numbers, x and y, are randomly selected, both from the interval [0, 10]. What is the probability that, at the same time, their sum is less than 7 and the absolute value of their difference is greater than 2?

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