Suppose that X₁, X₂, X3 are mutually independent random variables with the respective moment2generating functions, Mx, (t) = e²¹², Mx₂ (t) = e²t + 3t², and Mx₂(t) = (¹₂) ².1-2t,a) Calculate the probability that X₂ is between 2 and 4, P(2 < X₂ < 4).b)State with parameter(s) the probability distribution of Y = X₁ + X₂.c)Find the mean and variance of the statistic Y, ifi) Y = Σ=1 X.2ii) Y = 4X¹²4X₁²X3d)if y = X₁² + X3, what is the probability that Y is at most 12.833?2X1e)Find the value of such that P(Y > T) = 0.005, for Y=

As per bartlby guidelines we can answer only first three subpart and rest can be reposted

Answered: a) b) c) Calculate the probability that…

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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Dandelions have effects on crop production and lawn growth and are studied. In one region, the mean number of dandelions per square meter was found to be 10.8.Find the probability of no dandelions in an area of 1 m².P(X=0)=P(X=0)= Find the probability of at least one dandelion in an area of 1 m².P(at least one) = Find the probability of at most two dandelions in an area of 1 m².P(X≤2)=P(X≤2)=
Roll the correct die 100 times. Find: a) the average of the dropped points Enter the exact answer. а) M(X)= b) the variance of the amount of dropped points Enter numbers with a dot separator to one decimal place, for example 121.3. b) D(X)= c) the standard deviation of the sum of the dropped out points. Enter numbers with a dot separator to one decimal place, for example 12.3. c) σ (X) =
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000 miles of driving) of cars of a particular model varies Normally with mean 90 mg/mi and standard deviation of 4 mg/mi. A company has 25 cars of this model in its fleet. Find the level L such that the probability that the average NOX + NMOG level bar x for the fleet greater than L is only 0.03? Round final answer to three decimals.
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assume that X is normally distributed with a mean 160 and standard deviation of 45. find the probability that (A) x is less then 159 and (B) x is grater then 160
. What is the probability distribution if X~ B(3,0.82)? O P(X = 0) = 0.01 P(X = 1) = 0.08 P(X= 2) = 0.36 P(X = 3) = 0.55 O P(X = 0) = 0.55 P(X 1) = 0.36 P(X = 2) = 0.08 P(X = 3) = 0.01 P(X 0) P(X = 1) = 0.21 P(X 2) = 0.37 P(X = 3)3 0.61 = 0.03 P(X = 0) = 0.11 P(X = 1) = 0.20 P(X = 2) = 0.26 P(X = 3) = 0.43 %3D %3D
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=| S= (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…
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a) b) c) Calculate the probability that X₂ is between 2 and 4, P(2 < X₂ < 4). State with parameter(s) the probability distribution of Y = X₁ + X₂. Find the mean and variance of the statistic Y, if i) _Y = Σ=1 X. ii) Y = 4X₁² X3