Question

What is the difference between a continuous probability density function (pdf) and a discrete pdf and describe which type of pdf describes the Poisson distribution and which describes the exponential distribution.

Answer #1

Let X be a continuous random variable with probability density
function (pdf) ?(?) = ??^3, 0 < ? < 2.
(a) Find the constant c.
(b) Find the cumulative distribution function (CDF) of X.
(c) Find P(X < 0.5), and P(X > 1.0).
(d) Find E(X), Var(X) and E(X5 ).

2. Explain the difference between a continuous and a discrete
probability model. Give an example of each.

What is the difference between discrete variable and continuous
variable.

A random variable X takes values between -2 and 4 with
probability density function (pdf)
Sketch a graph of the pdf.
Construct the cumulative density function (cdf).
Using the cdf, find )
Using the pdf, find E(X)
Using the pdf, find the variance of X
Using either the pdf or the cdf, find the median of
X

Explain the difference between a discrete and a continuous
random variable.

describe the difference between discrete and continuous
variables, giving an example of each.
Explain why a correction for continuity is sometimes needed.

What is the difference between a continuous random variable and
a discrete random variable? In your own words, do not copy from the
internet. Please also give an example.

The lifetime X (in years) of a machine has a
probability density function (pdf):
?(?) =
??−?⁄?, ? > 0; ? > 0.
Find the value of the parameter ?. Give the two names of this
distribution.
Find E(X), Var(X), and
?(?5?−?⁄3).
Find the constant c such that P(X
> c) = 0.95.

Suppose a random variable X has cumulative distribution function
(cdf) F and probability
density function (pdf) f. Consider the random variable Y =
X?b
a for a > 0 and real b.
(a) Let G(x) = P(Y x) denote the cdf of Y . What is the
relationship between the functions
G and F? Explain your answer clearly.
(b) Let g(x) denote the pdf of Y . How are the two functions f
and g related?
Note: Here, Y is...

Which of the following is always true for all probability
density functions of continuous random variables?
A. They have the same height
B. They are bell-shaped
C. They are symmetrical
D. The area under the curve is 1.0
Like the normal distribution, the exponential density function
f(x)
A. is bell-shaped
B. approaches zero as x approaches infinity
C. approaches infinity as x approaches zero
D. is symmetrical

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