Q3) A) A grocery store sells X hundred kilograms of rice every day, where the distribution of the random variable X is of the following form:. x < 0 0sx < 3 3

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Q: (a) P(x ≤ 4), n = 6, p = 0.9 P(x) = (b) P(x > 5), n = 9, p = 0.6 I P(x) = (c) P(x < 3), n = 4, p =…

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Q: Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 =

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Q: Give the derivation of the variance for the binomial distribution.

A: X~Bin(n,p)

Q: (c) P(Z -2.15)

A:

Q: If a procedure meets all of the conditions of a binomial distribution except the number of trials is…

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Q: The PDF of the random variable X is fx (x)=-; 0<x<9. 6√x What are i) mean, ii) the mean square value…

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Q: Three components are randomly sampled, one at a time, from a large lot. As each component is…

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Q: (a) A lower bound for P(6<Y <24) (b) the value of k such that P(|Y-15| ≥k) ≤ 0.09.

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Q: Litter Size 1 2 3 4 5 6 7 8 9 Frequency 7 33 58 116 125 126 121 107 56 10 11 12 37 25 4

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Q: Suppose f(x), the pmf for a discrete random variable X is given in the table below: 10 15 f (x) |…

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Q: (1)A random variable is defined as 1/36(2x-1); x= 1,2,3,4,5,6     (a)Construct the Probability…

A: Random variable  X defined  as  fx=1362x-1   x=1,2,3,4,5,6∴fi=PX=xi         x1=1, x2=2,x3=3…

Q: а. Р(Х <- 2) b. Р(-1 <х < 1)

A:

Q: 3. Find the maximum likelihood estimator of 0> 0, using the random sample {X1,. , Xn}, whose…

A: # Given CDF of random variable x is  F(x)=1-e^-(x^2/2*theta)   : x&gt;0  then to find maximum…

Q: The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a…

A: Given, Te probability mass function is: 0 1 2 3 4 5 1/12 1/12 3/12 4/12 2/12 1/12     To…

Q: If a procedure meets all of the conditions of a binomial distribution except the number of trials is…

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Q: The Project Manager found that distribution of the amount of gravel (in tons) sold by a particular…

A: (As per the bartleby guidelines, for more than one question asked, only first one is to be solved.…

Q: (a) Discuss the two expressions 2(x₁ - x)² and (-1) 2(x,-)², both of which are used to measure the…

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Q: 9. Let X be a normally distributed random variable with a mean equal to 2 and a variance equal to 9.…

A: The last statement ( i.e. "E") Var(3X-2)=25 is incorrect one.

Q: b) Find the variance Var(X) of X.

A:

Q: A continuous random variable X is defined by: Solve: 1. f(x) = (3+x)²/16  ; -3≤ x≤ -1 2. f(x) =…

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Q: Ifa is a binomial random variable, compute P(x) for each of the following cases: (a) P(x ≤ 4), n =…

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Q: fx(x)={12/11(1−x2) −1/2≤x≤1/2 0 otherwise Random…

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Q: a)Given a random variable with pgf G (s) = (s+1) %3D (2s+3). Find the mean, variance and qk = Prob…

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Q: If X is a random variable with Binomial distribution of n=35 and p=0.45, find: i. E(X) ii. Var(X)…

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Q: If a procedure meets all of the conditions of a binomial distribution except the number of trials is…

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A: Given data is xi P(xi) -2 0.1 0 0.2 5 0.2 8 0.3 10 0.2

Q: If X is a random variable with Binomial distribution of n=35 and p=0.45, find:    i. E(X) ii.…

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Q: 5) Let Y be binomial (n =4, II= .3) (a) Calculate the mean and variance by filling in the following…

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Q: For an experiment, roll 2 fair dice. Let the random variables, X = sum of the 2 dice  Y = larger…

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!