In a physical experiment, there are 104 elementary particles under consideration. During the experiment, each particle decays independently of each other with a probability of 10−3. Let X be a random variable that tells the number of decays. (a) What is the distribution of X? Write an exact expression for the point probability P(X = k) when the probability is positive (when is this the case?). (b) Calculate the numerical approximation of the expression for the point probability P(X = k) to four significant figures in the cases k = 0, k = 2 and k = 10.

In a physical experiment, there are 104 elementary particles under consideration. During the experiment, each particle decays independently of each other with a probability of 10−3. Let X be a random variable that tells the number of decays. (a) What is the distribution of X? Write an exact expression for the point probability P(X = k) when the probability is positive (when is this the case?). (b) Calculate the numerical approximation of the expression for the point probability P(X = k) to four significant figures in the cases k = 0, k = 2 and k = 10.

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

In which probability distribution would a random variable XX have E(X)=λE(X)=λ?
A deck has only 51 cards left, because a spade has been removed. From this deck, cards will be drawn at random, in succession, without replacement. Let Xi be a random variable representing the number of spades in the future i th draw. Calculate the following, and present your answer with 5 digits after the decimal point: Prob(X1 + ... + X7 = 3) = [1]
İf X follows the Poisson probability law such that P (xr 1) = P (x = 2). then ind the probability of 4 successes.
Give the formula for p(x) for a binomial random variable with n= 6 and p = 0.4. -.. - O'O (x=0, 1, 2 ...D p(x) = (Simplify your answers. Use integers or decimals for any numbers in the equation.)
The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.
İf X follows the Poisson probability law such that P (xr 1) = P (x = 2). then ind the probability of 4 successes.
Answer no. 1 only
A committe of size 3 to be selected at random from 4 chemists and 5 physicists , Find the probability that : E (x)=? а- 16/9 b- 15/9 с-3/4 d- 8/7 e- 4/3
A box in a supply room contains 24 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-watt, and 7 are rated 23-watt. Suppose that three of these bulbs are randomly selected. (Round your answers to three decimal places.) *****-+ in the probability it exactly two of the selected hulhe 1 na is the ph that all the -ina? "'? (d) If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs?
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 2 breakdowns every 428 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and Ux. (Write the fraction in reduced form.) ux = f(x) = 214 (b) Write the formula for the exponential probability curve of x. P(x <4) ✔ Answer is complete and correct. 1 P(115
Event A is my wife cooking dinner tonight. It has been determined that P(A) = 0.15. What is P(not A)?
İf X follows the Poisson probability law such that P (xr 1) = P (x = 2). then ind the probability of 4 successes.