Question
In: Statistics and Probability
A random variable has a triangular probability density function with a = 50, b = 375,...
A random variable has a triangular probability density function with a = 50, b = 375, and m = 250.
What is the probability that the random variable will assume a value between 70 and 250? If required, round your answer to four decimal places.
| What is the probability that the random variable will assume a value greater than 280? If required, round your answer to four decimal places. |
Solutions
orchestra answered 1 year agoRelated Solutions
For ? continuous random variable has ??(?) probability density function with ? e. Define ?(?)=?.... ??...
For ? continuous random variable has ??(?) probability density
function with ?
e. Define ?(?)=?.... ?? =(.,.)
f. Obtain ? constant.
g. Calculate the ?(?), ???(?) values.
h. Define 5 probabilities and calculate them.
Assume that a continuous random variable has a following probability density function: f ( x )...
Assume that a continuous random variable has a following
probability density function:
f ( x ) = { 1 10 x 4 2 ≤ x ≤ 2.414 0 o t h e r w i s e
Use this information and answer questions 3a to 3g.
Question a: Which of the
following is a valid cumulative density function for the defined
region ( 2 ≤ x ≤ 2.414)?
A.F x ( x ) = 1 50 x 5 −...
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,...
The probability density function of the continuous random variable X is given by fX (x) =...
The probability density function of the continuous random
variable X is given by
fX (x) = kx, (0 <= x <2)
= k (4-x), (2 <= x <4)
= 0, (otherwise)
1) Find the value of k
2)Find the mean of m
3)Find the Dispersion σ²
4)Find the value of Cumulative distribution function FX(x)
The probability density function of the random variable X is given by fX(x) = ax +...
The probability density function of the random variable X is
given by fX(x) = ax + 2/9 if 1/2 ≤ x ≤ 3, and 0 otherwise.
(a) Compute the value of a.
(b) Let the random variable Y be defined as Y = [X], where [·]
is the “round down” operator (that is, for example, [2.5] = 2,
[−2.5] = −3, [−3] = −3). Find the probability mass function of Y .
(Hint: For Y to take value k, what...
The random variable Y has an exponential distribution with probability density function (pdf) as follows: f(y)...
The random variable Y has an exponential distribution with
probability density function (pdf)
as follows:
f(y) = λe−λy, y >0
= 0, otherwise
(i) Showing your workings, find P (Y > s|Y > t), for s ≥
t. [3]
(ii) Derive an expression for the conditional pdf of Y ,
conditional on that Y ≤ 200. [3]
N(t) is a Poisson process with rate λ
(iii) Find an expression for the Cumulative Distribution
Function (CDF) of the waiting time until...
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 )
=
Let X be a continuous random variable with a probability density function fX (x) = 2xI...
Let X be a continuous random variable with a probability density
function fX (x) = 2xI (0,1) (x) and let it be the function´ Y (x) =
e −x
a. Find the expression for the probability density function fY
(y).
b. Find the domain of the probability density function fY
(y).
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