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In: Statistics and Probability
If the random variable x~N(0,c^2), and g(x)=x^2, find and sketch the distribution and density function of...
If the random variable x~N(0,c^2), and g(x)=x^2, find and sketch the distribution and density function of the random variable y=g(x).
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orchestra answered 1 year agoRelated Solutions
A continuous random variable X, has the density function f(x) =((6/5)(x^2)) , 0 ≤ x ≤...
A continuous random variable X, has the density function f(x)
=((6/5)(x^2)) , 0 ≤ x ≤ 1; (6/5) (2 − x), 1 ≤ x ≤ 2; 0, elsewhere.
(a) Verify f(x) is a valid density function. (b) Find P(X > 3 2
), P(−1 ≤ X ≤ 1). (c) Compute the cumulative distribution function
F(x) of X. (d) Compute E(3X − 1), E(X2 + 1) and σX.
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
1. Let X be random variable with density p(x) = x/2 for 0 < x<...
1. Let X be random variable with density p(x) = x/2 for 0 < x < 2 and 0 otherwise. Let Y = X^2−2.
a) Compute the CDF and pdf of Y.
b) Compute P(Y >0 | X ≤ 1.8).
Given the cumulative distribution of an exponential random variable find: The probability density function Show that...
Given the cumulative distribution of an exponential random
variable find:
The probability density function
Show that it is a valid probability function
The moment generating function
The Expected mean
The variance
Given the cumulative distribution of a gamma random variable find: The probability density function Show that...
Given the cumulative distribution of a gamma random variable
find:
The probability density function
Show that it is a valid probability function
The moment generating function
The Expected mean
The variance
1. The random variable X has probability density function: f(x) = ( ke−x 0 ≤ x...
1. The random variable X has probability density function: f(x)
= ( ke−x 0 ≤ x ≤ ln 5 4 0 otherwise Part a: Determine the value of
k. Part b: Find F(x), the cumulative distribution function of X.
Part c: Find E[X]. Part d: Find the variance and standard deviation
of X. All work must be shown for this question. R-Studio should not
be used.
The random variable X has probability density function: f(x) = ke^(−x) 0 ≤ x ≤ ln...
The random variable X has probability density function: f(x) =
ke^(−x) 0 ≤ x ≤ ln (5/4) 0 otherwise Part a: Determine the value of
k. Part b: Find F(x), the cumulative distribution function of X.
Part c: Find E[X]. Part d: Find the variance and standard deviation
of X. All work must be shown for this question.
The random variable X has a continuous distribution with density f, where f(x) ={x/2−5i f10≤x≤12 ,0...
The random variable X has a continuous distribution with density
f, where f(x) ={x/2−5i f10≤x≤12 ,0 otherwise.
(a) Determine the cumulative distribution function of X.(1p)
(b) Calculate the mean of X.(1p)
(c) Calculate the mode of X(point where density attains its
maximum)
(d) Calculate the median of X, i.e. a number m such that P(X≤m)
= 1/2
(e) Calculate the mean of the random variable Y= 12−X
(f) Calculate P(X^2<121)
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