Question
In: Statistics and Probability
The density of a random variable X is given by f(x)=(3x^2, o less than x less...
The density of a random variable X is given by f(x)=(3x^2, o less than x less than 1, or f(x)=0, otherwise Let Y=e^x (a) find the density function of Y(b) find E(Y) two ways:(i)using the density of Y and (ii) using the density of X
Solutions
orchestra answered 2 years agoRelated Solutions
A random variable X has a density given by f X ( x ) = (1...
A random variable X has a density given by
f X ( x ) = (1 −
x^2 ) [ u ( x ) − u (
x − 1) ] + aδ ( x − 2 )where
u(x) is the unit step function and δ(x)
is a delta function.
a). Find the value of a, E(X) and σ
δx^2 .
b). Find and make a labeled sketch of
FX (x) .
C). W = the event {X ≥ 0.5}....
2 Consider the probability density function (p.d.f) of a continuous random variable X: f(x) = (...
2 Consider the probability density function (p.d.f) of a
continuous random variable X: f(x) = ( k x3 , 0 < x < 1, 0,
elsewhere, where k is a constant. (a) Find k. (b) Compute the
cumulative distribution function F(x) of X. (c) Evaluate P(0.1 <
X < 0.8). (d) Compute µX = E(X) and σX.
Suppose that a random variable X has a pdf f(x) = ke^(-3x^2+6x-5), -infinity < x <...
Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity
(a) Find k.
(b) Find the mean and variance of X.
(c) Find the probability that X is between 1 and 1.5.
Suppose that a random variable X has a pdf f(x) = ke^(-3x^2+6x-5), -infinity < x <...
Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity
(a) Find k.
(b) Find the mean and variance of X.
(c) Find the probability that X is between 1 and 1.5.
Suppose that a random variable X has a pdf f(x) = ke^(-3x^2+6x-5), -infinity < x <...
Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity
(a) Find k.
(b) Find the mean and variance of X.
(c) Find the probability that X is between 1 and 1.5.
Suppose that a random variable X has a pdf f(x) = ke^(-3x^2+6x-5), -infinity < x <...
Suppose that a random variable X has a pdf
f(x) = ke^(-3x^2+6x-5), -infinity < x < infinity
(a) Find k.
(b) Find the mean and variance of X.
(c) Find the probability that X is between 1 and 1.5.
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.
Consider a continuous random variable X with the probability density function f X ( x )...
Consider a continuous random variable X with the probability
density function f X ( x ) = x/C , 3 ≤ x ≤ 7, zero elsewhere.
Consider Y = g( X ) = 100/(x^2+1). Use cdf approach to find the cdf
of Y, FY(y). Hint: F Y ( y ) = P( Y <y ) = P( g( X ) <y )
=
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)
R Code 2. Suppose X is a random variable with density f(x; ψ) = 2ψ-2 xI(0...
R Code
2. Suppose X is a random variable with density f(x; ψ) = 2ψ-2
xI(0 ≤ x ≤ ψ), where ψ > 0 is a parameter.
(a) Draw a graph of the density when ψ = 3 in R.
(b) Write a function called genTri that generates n independent
realizations of X. The function should take the arguments n and psi
and return a vector of n realizations. Make a histogram of n = 104
realizations and compare the...
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