Problem#1: Find the expectation, variance and standard deviation of each of thefollowing distributions:a.)2311f(x)11b.)-5-4112f(x)8.c.)1345f(x)0.40.10.20.3

Part a. Given : Convert data in decimal : Expected value : Thus expected value is 4 Variance :…

Answered: Problemi1: Find the expectation,…

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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x f(x) 20 0.10 25 0.20 30 0.25 35 0.15 40 0.10 a. What is the probability that the firm will obtain 40 or more new clients? b. What is the probability that the firm will obtain fewer than 35 new clients? c. find expected vaule= variance= standard deviation =
Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)
A company manufactures products in its factory in Turkey for sale in Asia. Products sold in different countries differ in terms of the power outlet as well as the language of the manuals. Currently, the company assembles and packs products for sale in individual countries. The distribution of weekly demand in different countries is normally distributed with means and standard deviations as shown in the table Assume that demand in countries to be independent. Given that the lead time from the Turkey factory is (X/4) weeks, how much safety inventory does the company require in Asia if it targets a CSL level of 95 percent?X= 96 b. The company builds a distribution center in Asia. It will ship base products to this center. When an order is received, the center will assemble power supplies, add manuals, and ship the products to the appropriate country. The base products are still to be manufactured in Turkey with the same lead time. How much saving of safety inventory can the company expect…
Let Y, represent the ith normal population with unknown mean #, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S² = (₁-P) ². (d) Define V₁, a function of S1, that has a chi-square distribution. (e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument. (f) Find a (1-a) x 100% confidence interval for of
If the random variable X as a mean of u and a variance of o2 what is the P((X-u)² < 20): O less that equal to 1/4 O greater than or equal to 3/4 cannot tell O equal to 5/4
I need help with C and D
Q.6 (a) Write the gamma distribution for a random variable X denoted by X~F(a, B); its mean, variance and moment generating function (No derivation is required). (b) What is the relationship between gamma distribution and chi-square distribution?
I have problem in the question number #2, but the answer is with the result of question number #1
Prob.5 Find the mean, the median, and the mode of the random variable X with the following probability density functions: (a) Gaussian distribution with parameters μ and o². (b) Exponential distribution with parameter 1. (c) Beta distribution with a = 3 and b = 4. (d) Uniform distribution in the interval (a, b).
Example 9-4. X is a normal variate with mean 30 and S.D. 5. Find the probabilities (i) 26 45, and (iii) |X – 30l > 5.

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Problemi1: Find the expectation, variance and standard deviation of each of the following distributions: a.) 3 11 f(x) b.) -5 -4 f(x) c.) 1 4 f(x) 0.4 0.1 0.2 0.3 -- IN m IN 2-13