Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street crossing is a randomvariable with the following pdf.f(x) = {1; (1 − x/68)³ 0 ≤ x < 68otherwiseIf you use this crossing every day for the next 10 days, what is the probability that you will wait for at least 10seconds on exactly 4 of those days?

The random variable represents the waiting time for the pedestrian signal. The PDF of random…

Answered: Suppose that the waiting time X (in…

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...

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(5) If Xis a r.v. with mean u and variance o?, using Chebyshev's-Inequality, AX-2 20) S (a) 0.5 (b) 0.05 (c)0.657 (d) 0.25.
A random sample of size n₁ = 14 is selected from a normal population with a mean of 76 and a standard deviation of 7. A second random sample of size n₂ = 9 is taken from another normal population with mean 71 and standard deviation 11. Let X₁ and X₂ be the two sample means. Find: (a) The probability that X₁ – X₂ exceeds 4. 1 2 (b) The probability that 4.3 ≤ X₁ – X2 ≤ 5.6. Round your answers to two decimal places (e.g. 98.76). (a) i (b) i
7. Prove or disprove that the following function is a cumulative distribution function (cdf). If the function is a cdf, is the random variable continuous or discrete? Why? (Note: This is a special case of a logistic distribution.) Fx(x)= 1 1+ e-z -∞<<∞.
8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable X that follows an exponential distribution with mean 15 minutes. a) Find P(14 < X < 22). Round off your answer to two decimal places. x 22 1 P(14 < X <22) = √₂/1² 15 e 15dx = P(x < 22) — P(x < 14) x 15 122 = e 15 22 1 - e 14 or 0.8 = = 22 14 = −e 15 + e15 = 0.16254≈ 0.16 - (1 – b) Find the 80th percentile. Round off to the nearest whole number. 1 X S 15 14 e 15 t e 15 dt X 0.8 = 1 e 15 X e 15 = = 0.2 14 22 = e 15 e 15 = 0.16 x — = ln (0.2). This gives x = 24.14156 15
3. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
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
Suppose Xt denotes the unknown whose value is the success count for ?ttrials of a Bernoulli Process with success rate p and Wn the unknown whose value is the number of trials to have the nth success. Then, the probability that the number of trials to get the 7th success is at most 10 is which of the following? (A) P(X10≥7)P(X10≥7) (B) P(X7<10)P(X7<10) (C) P(X10<7)P(X10<7) (D) P(W7≥10)

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