For x1, the marginal distribution fx1 (x1) function is valid is it a density function)

Q: therwiSe Is this a proper density function of a continuous random variable?

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Q: The random variables X and Y are related as Y= X. Find the density function of voriable Y.

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Q: total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one…

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Q: Let sinx 0 <x<n f(x) = otherwise be probability density function of X, Compute var(x)?

A: The variance of X is defined as Var(X) = E(X2) - (E(X))2

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Q: A continuous random variableX that has a density function given by for 1<r < 4 | f(x) = elsewhere…

A: We have given that  Probability density function  f(x)= 1/5    ,- 1 &lt;x&lt; 4

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Q: f we consider the function f (x) = x2 (with x = position) as a probability density distribution…

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Q: Suppose the random variables Yi and Y2 have juint probability density Function Flg,yz),given by:…

A: # joint pdf of (y1,y2) is given  f(y1,y2)=6y^2*y2     : 0&lt;y1&lt;y2 ,y1+y2&lt;2  then to write the…

Q: (a) Find the marginal density function for Y,. f2(Y2) = , where (b) For what values of y, is the…

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Q: Suppose that X ~ N(0,1). Then, under the condition X =x for some I E R, the distribution of Y is…

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Q: The probability density function of the gamma distribution is as follows. f (x) = Г(а) ßx , x>0, a,…

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Q: If X has density f (x) = 1 – |æ| for |æ| < 1 then Var (X) =

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Q: Assume that X has density f (x) = cx² (3 – x) for –2 <x < 3. %3D What is the distribution function…

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Q: (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional…

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Q: A large company has determined that the function f (x) = 3x, 0 <x<1 serves as a payroll density…

A: Answer : The value of G=0.5

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Q: Verify that f(x) is a density function and find also the mean of X.

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Q: Find the marginal density function fx, (x1) of X1.

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Q: then what is the marginal density function of X, where nonzero?

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Q: Find the marginal density functions of X and Y.

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Q: Let X have the uniform distribution on the interval [1, 3]. Find the density function of Y =X^2.

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Q: 1 'If fx(x)=- -x² /2 find the density function for Y

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Q: Suppose that X is a continuous unknown all of whose values are between -5 and 5 and whose PDF,…

A: It is given that the X is a continuous random variable with pdf f(x) = c( 25 -x2 ) , − 5 ≤ x ≤ 5 ,…

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!