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

Q: (a) P(X2 189) = (Round to four decimal places as needed.) (b) What does the result from part (a)…

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Q: Suppose a continuous random variable X has the following CDF::  F(x) = 1 - 1/ (x+1)4, x > 0. Find SX…

A: We have given, A continuous random variable X has the following CDF: F(x) = 1 - 1x+14, x &gt; 0.

Q: Suppose that X is a random variable which only takes on non-negative values, with mean 5 and…

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Q: 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 3)

A: Given Data: Var(X)=5 Equation: Var(4X-3) ......(1) Simplify the equation (1). Var4X-3=42VarX=16VarX

Q: Q2 (a) List all possible simple random samples of size n= 2 that can be selected from the population…

A: 1) list of all possible simple random samples of size 2 can be selected from the {0,1,2,3,4}.…

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: For the random variable X, E(X+1) = 3 , E(X- +X)= 9 then the value of Var(X) is 10 3 0 2 0 50

A: Given, E(X+1)=3 Then E(X)+1=3          E(X) =2 and E(X2+X)=9       E(X2)+E(X)=9       E(X2)+2=9…

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

A: Solution:It is given that probability that someone is a universal donor​ (with group O and type Rh…

Q: For a random variable X, suppose that E[X] = 2 and Var(X) = 4. Then (a) E[(4 + x)²] = (b) Var (5+5X)…

A: Given,E(X)=2Var(X)=4we know that…

Q: is known that 26% of adults in the uk use a certain app, A Researcher selects a random s lults in…

A: X number of adults in sample who use app will follow binomial distribution with n = 5000 and p =…

Q: Suppose that X₁, X2, X3 are independent and identically distributed random variables with…

A: Solution

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

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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 =…

A: We know that, Probability mass function for binomial distribution is, P(X= x) = nCx*(p)x*(1-p)n-x…

Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

A: Solution

Q: X and Y are random variables that are both Normally Distributed. The Mean of X is 5 and its SD is 3.…

A: Given that  P(4 &lt; Y &lt; 16) = P(A &lt; X &lt; B) μX=5σX=3μY=-2σY=6

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

A: The probability that the first subject to be a universal blood donor is the fifth person selected is…

Q: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 27 psi.…

A: As per our guidelines we are supposed to answer only 3 subparts of any questions so i am solving…

Q: Let X1 , X2 , X3  be  a collection of independent discrete random variables that all take the value…

A: Sampling distribution of proportion: From the central Limit theorem, the sampling distribution of…

Q: A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and…

A: X : voltage of a noisy resistor    Therefore,  X ~ N(mean : μ = 0, standard deviation : σ = 2 =…

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

Q: Suppose that X₁, X2, X3 are independent and identically distributed random variables with…

A: Given Cdf  F(x)=1-2-x; x≥0

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: Given Information: Consider X, Y and Z are jointly distributed random variables. Consider the…

Q: Suppose that three random variables x,„X,„X, fom a random sample from the uniform distribution on…

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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!