Consider the following two probability distributions: g(x) = 5! (0.99) (0.01) 5- x! (5-x)! x = 0, 1, 2, 3, 4, 5 " 20000 f (x) x > 0 " (x+100) (a) Considering f(x), determine P(x >= 2.0) and P(0.5 < x < 1.5). (b) Considering g(x), determine P(x = 2), P(1 < x < 4) and P(x >= 5)
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- 1. Let X be the mean of a random sample of size n = 64 from the exponential distribution e-2/², x>0 otherwise 0, f(x)= = Based on central limit theorem, approximate the probability P (1.8 < X < 2.1). Round your final answer to 4 decimals.The pdf of the time to failure of an electronic component in a copier (in hours) is f (x) = [exp (-x/3100)]/3100 for x > 0 and f (x) = 0 for x ≤ 0. Determine the probability that:(a) A component lasts more than 1180 hours before failure.(b) A component fails in the interval from 1180 to 2010 hours.(c) A component fails before 3010 hours.(d) Determine the number of hours at which 11% of all components have failed.(e) Determine the mean.Round your answers to three decimal places (e.g. 98.765).Verify that the following function is a probability mass function, and determine the requested probabilities. Answer rounded-off to 4 decimal places f(x)=(125/31)(1/5)* P(X>1)=_ 7 x={1,2,3}
- Establish the following: 0P (E)1 , P (A u B) = P (A) + P (B) – P (A n B) , P (A) = 1 – P (A’) ii The probability that a boy with a catapult hits target A is 2/3and that he hits target B is ¾. Given the probability of hitting both targets to be 1/2, find the probability that he (a) hits at least one of the targets (b) does not hit any. iii What is the probability of having at least one 6 in three throws with a dice?A continuous random variable X has probability distribution function f(x) , wheref(x) = k(1 − x2) for − 1 < ? < 1. Calculate the P(X < 0)?Prof that' For a fixed B with P(B) > 0, P(A l B) is probability function.
- I need help finding the probability that only two cars arrive.(50) Let X be a random variable with p.d.f. k 1If F(x) is cumulative distrbution function of a continuous random variable X, the probability (function f(x) is the dervative of F(x (Fa)se (TrụeRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON