5. There are four marbles numbered 1,2,3,4 in a jar. Two returnable marbles are drawn fromthe jar. Let x be the random variable representing the absolute value of the differencebetween the squares of the numbers on the drawn marbles.a) Find the expected value of the random variable (2X+4).b) Calculate the variance and standard deviation of the random variable (2X+4).

Probability is defined as the total number of favorable cases of an event divided by the total…

Answered: re are four marbles numbe ed 1,2,3,4 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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The fracture strength of bi-tempered glass averages 14.03 (measured in thousands of pounds per square inch) and has standard deviation 2. Suppose we randomly select 100 pieces of bi-tempered glass. Let M be the random variable representing the mean fracture strength of the 100 selected pieces. Let T be the random variable representing the sum of the fracture strengths of the 100 selected pieces. Using R and write the code outa) What theorem will let us treat T and M as approximately normal random variables? Monte Carlo TheoremLaw of Large Numbers 301 TheoremCentral Limit TheoremChebychev's TheoremConvolution Theorem b) What is the expected value of T? c) What is the standard deviation of T? d) What is the approximate probability that T is greater than 1400? e) What is the 98th percentile of the approximate distribution of T? f) What is the standard deviation of M? g) What is the approximate probability M is greater than 13.99? h) What is the variance of 93M?
Total blood volume (In ml) per body welght (In kg) is Important In medical research. For healthy adults, the red blood cell volume mean is about u = 28 ml/kg.t Red blood cell volume that is too low or too high can Indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows. 32 26 40 37 31 35 29 Let x be a random varlable that represents Roger's red blood cell volume. Assume that x has a normal distribution and o = 4.75. Do the data Indicate that Roger's red blood cell volume is different (either way) from u = 28 ml/kg? Use a 0.01 level of significance. (a) what is the level of significance? State the null and alternate hypotheses. Will you use a left-talled, nght-taled, or two-talled test? O Ho: H= 28 ml/kg; H: H> 28 ml/kg; right-tailed O Hg: H- 28 ml/kg; H: u = 28 ml/kg; two-taled O Ho: H- 28 m/kg; H: H 23 2$ backspace 1 4. 8 9.
5.
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