If X has a binomial distribution with n=3 and p =; , find the probability distribution of Y = 1+ X Then calculate E(Y) and V(Y).

Q: Let X be a stochastic variable with a N(8,16) distribution. Suppose P(X<b) = 0.719. Calculate the…

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Q: The random variable X is exponentially distributed, where X represents the waiting time to see a…

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Q: Find the mean and variance of the uniform probability distribution given by f(x)=1/n for x=1,2,3,4……

A: Given pdf is: f(x)=1n    for x=1,2,3,4.....

Q: Suppose Y has a uniform pdf over the interval [3,5]. Find its (1) first quartile, its (2) median,…

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Q: Find UCL, LCL for a 'c' chart when u. = 6.0 and u. = 12.5 with 0.995 and 0.005 probability limits.

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Q: Find the distribution function of the random variablethat has the probability distribution f(x) =…

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Q: Let X, and X, be independent exponential distributions with the same parameter 1. What is the joint…

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Q: Suppose that the hazard rate of a certain continuous positive random variable is given by 4t+4. Find…

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Q: assume that X is normally distributed with a mean 135 and standard deviation of 45. find the…

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Q: because all airline passengers do not show up their reserved seat, an airline sells n = 125 tickets…

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Q: What is the probability that a randomly selected American adult has never been tested? Show work.…

A: From the given information, N(NT)=134,767 and N(T)=77,789.

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a no random variable…

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Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…

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Q: For a highway, the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X is…

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Q: A fair 20-sided die is tossed. If X denotes the random variable giving the number on the bottom face…

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Q: The random variable x follows a uniform probability distribution in the interval (0,1); the…

A: We know that  The pdf of Uniform distribution is  f(x) = { 1/(b-a) ,   a&lt;x&lt;b                0.…

Q: The random variable X is exponentially distributed, where X represents the waiting time to see a…

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Q: Let the random variable X fit the binomial distribution with p=1/2 , n=3 parameters. Plot the…

A: Given Data: n=3 p=0.5   Distribution function is also known as cumulative function

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Q: Suppose random variable X has a Poisson distribution with t​ = 2 and λ= 4. What is​ E(X)?

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Q: assume that X is normally distributed with a mean 1550 and standard deviation of 75. find the…

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Q: assume that X is normally distributed with a mean 210 and standard deviation of 60. find the…

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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: X and Y be standard normal random variables with correlation ρ. Compute the joint and marginal…

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Q: If X is exponentially distributed with a mean of 3, can you find a uniform distribution U[a,b] with…

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Q: Find the standard deviation of a discrete random variable X which satisfies P(X=1)=0.1,P(X=-1)=0.6,…

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Q: The number of cracks that need repair in a section of interstate highway follows a Poisson…

A: For a discrete random variable X ~P(m) the pmf is given as :   P(X=x) = e-mmxx!      , x=0,1,2,3,...…

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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.…

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Q: et X be a random variable with the following probability distribution. Valuex of X P(X=x) -30 -20…

A: let X be a random variable with the following probability distribution.

Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)).…

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Q: Please Find the mean and variance of Binomial variable X having p=0.09 and n=2.

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Q: Assume that x has a normal distribution with the mean=4 and standard deviation=6. Find the…

A: It is given that, X has a normal distribution with mean, μ =4 and standard deviation, σ =6.

Q: For the probability distribution, find a. X b. P(y> 2) c. F(y = 6) d. Du 0.05, 0.10, f(y)= 0.15,…

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Q: Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.

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Q: the time X that a lightbulb can last (life lenght) is a distribution with mean 1 year and standard…

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Q: Let X be a binomially distributed random variable B(n, p) with E(X) = 2 and Var(X) = 4/3. Find n.

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Q: Suppose X is a random variable of a normal distribution with E(X)=2 and Var(X)=4. Find P(X<4)

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Q: Find the probability for P(y 3) if y is distributed as N(1, 9)

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Q: Assume that ξ has a rectangular distribution with the mean value E(ξ) = 0 and the variance V(ξ) =…

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Q: Find the approximate mean and variance of Y = √X, where X is a random variable following a Poisson…

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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!