Suppose the random variable X has the following probability density function f (2) = 2 %3D otherwise What is the expected value of X?

Q: If the probability density function of a continuous random variable X is 0.50x 0<c< 2 0 <x f (2) = {…

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Q: 1<x < 3 | f(x) = {C(x - 1)(3 – x) diğer

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Q: If the probability density function of the random variable X is S1- |a| for |æ| < 1 f (x) = { 0, el…

A: The equation to find out the variance of a continuous random variable , when the PDF is given is ,…

Q: Suppose that random variable X is uniformly distributed between 5 and 29. Draw a graph of the…

A: The distribution of X follows uniform with a=5 and b=29.

Q: Suppose that the continuous random variable X has a probability density function, given by: Find…

A: Expectation of a Continuous Random Variable: The expectation of a continuous random variable X,…

Q: If Z is a random variable from a standard normal distribution and if P(Z < a) = 0.7, then P(Z <= a)…

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Q: 6. The pH water samples from a specific lake is a random variable X with probability density…

A: a) fx=387-x2, 5≤x≤7 EX=∫57xfxdx       =∫57x*387-x2dx      =38*443      =112

Q: You are given the following random observations: 0.1 0.2 0.5 1.0 1.3 You test whether the sample…

A: Given random observations are 0.1, 0.2, 0.5, 1.0, 1.3. The probability for obtaining above values…

Q: If ZZ is a random variable from a standard normal distribution and if P(Z &gt; c) = 0.21, then P(Z…

A: From the given information, P(Z&gt;c)=0.21 and , P(Z&lt;c–)=0.21The normal distribution is a…

Q: Given the random variable X and it's probability density function below, find the standard deviation…

A: Calculate E[X]  x P(x) x*P(x) -1 0.40 -0.40 0 0.10 0 2 0.20 0.40 4 0.30 1.20 Total/…

Q: The total area of a normal probability distribution is dependent on a value of z approximated by the…

A: Normal distribution is a distribution whose curve is bell shaped and the distribution is symmetric…

Q: 1. The random variable Y = X2 does not have a normal distribution because the probability density…

A: Given that,  X~ N(u,σ2)  Where u is mean and σ2 is variance of X.  P.d.f. of X is given by,    Y= X2

Q: Consider the experiment of rolling 2 dice and define Y to be the A.V. that record the sum of the…

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Q: Consider the following probability density function for a random variable X. 2 1sx54 S(x) =9 10…

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Q: If a random variable has a probability density function given by fox) =3 for 4.9 sxs5.1. Then the…

A: The distribution function of X is defined as F(x) = P(X ≤ x)

Q: Suppose the probability density function for a uniform distribution ranging from 0 to 1. The mean of…

A: Solution: 5. Let X be the length of statistics professor class. From the given information, X…

Q: Suppose the probability density function for a uniform distribution ranging from 0 to 1. The mean of…

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Q: 7. If X is an exponential random variable with parameter B = 1, find the probability density…

A: Given problem is :

Q: Find (by inspection) the expected values and variances of the exponential random variables with the…

A: it is given that x is a exponential random variables with pdf, a) fx = 3e-3x b) fx = 14e-x4

Q: Consider the following joint probability density function of the random variables X and Y. Are X and…

A: Given: f(x,y)=3x-y9       1&lt;x&lt;3, 1&lt;y&lt;20                  elsewhere

Q: In Exercise, a probability density function of a random variable is defined. Find the expected…

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Q: 2. Let X be a random variable with the a normal probability density function (with known mean and…

A: We have given that X be a random variable with a normal probability density function ( known mean…

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Q: The number of large cracks in a length of pavement along a certain street has a Poisson distribution…

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Q: Find the expected value of the random variable Xwhose probability density is given by f(x) =⎧⎪⎪⎨⎪⎪⎩x…

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Q: Calculate the standard deviation o of X for the probability distribution. (Round your answer to two…

A: Obtain the standard deviation of X for the probability distribution. The standard deviation of X for…

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Q: Let X be a discrete random variable with probability mass function given in the following table: 2 3…

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Q: If is a Gaussian random variable withµ mean and o2 variance, find the probability density function…

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Q: The probability density function for a uniform distribution ranging between 11.975 and 12.100 is

A: From the provided information, The range of uniform distribution are a = 11.975 and b = 12.100

Q: Let X be a discrete random variable with probability mass function given in the following table: 4 5…

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Q: Let the life span of a material be given by the probability function f(x)=c²xe^(-cx)  (x≥ 0).…

A: Probability function  f(x) = c2xe-cx       x≥0

Q: Consider the following probability density distribution of random variable X. if 0<x < 6 f(x) = }kx…

A: Given function is f(x)={k            if 0&lt;x&lt;6kx+3k   if 6&lt;x&lt;100                otherwise

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A: we have to find  true or false

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Q: The probability density function of a discrete random variable X is given by the following table:…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: If X is normally distributed with mean 0 and variance 1, what is the probability density function of…

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Q: Suppose that random variable X is uniformly distributed between 5 and 25. Draw a graph of the…

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Q: Suppose the probability density function for a uniform distribution ranging from 0 to 1. The mean of…

A: Given Information:  The uniform distribution is ranging from 0 to 1.

Q: ollowing is the probability distribution for the   random variable X        X             0…

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Q: сх с +—,0 <х<3 2 0, f(x) = otherwise О а. 1/3 ОЬ. 4/9 О с. 2/15 2/9

A: We know that , the probability density function is equals to 1.

Q: 7. If X is an exponential random variable with parameter B = 1, find the probability density…

A: Given :X is an exponential random variable with parameter β=1,find the probability density functin…

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A: (a) Pdf of normal distribution -∞&lt;x&lt;∞…

Q: If the probability density function of random variable X is given by: = {k(x-1)(2-x), 0, 15xS 2;…

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Q: A continuous random variable x is normally distributed with a mean of 1 and a standard deviation of…

A: Given Mean μ=1, standard deviations σ=0.2  X~N(μ=1, σ=0.2) P(X=0.5)=?

Q: [1] The probability density function of a random variable X is SC(x + 4), -4 4.

A: Note: Hey there! Thank you for the question. As you have posted several different questions…

Q: If F(x) is cumulative distrbution function of a continuous random variable X, the probability…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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!