Question

A random variable XX with distribution
Exponential(λ)Exponential(λ) has the **memory-less
property**, i.e.,

P(X>r+t|X>r)=P(X>t) for all r≥0 and t≥0.P(X>r+t|X>r)=P(X>t) for all r≥0 and t≥0. |

A postal clerk spends with his or her customer has an exponential distribution with a mean of 3 min3 min. Suppose a customer has spent 2.5 min2.5 min with a postal clerk. What is the probability that he or she will spend at least an additional 2 min2 min with the postal clerk?

Answer #1

X: time spent by a postal clerk with customer.

given that ,

the pdf of the distribution is:-

**the probability
that he or she will spend at least an additional 2 min with the
postal clerk be:-**

[ using memory-less property]

*** if you have any doubt regarding the problem please write it
in the comment box.if you are satisfied please give me a
**LIKE** if possible..

Let X be an exponential random variable with parameter λ > 0.
Find the probabilities P( X > 2/ λ ) and P(| X − 1 /λ | < 2/
λ) .

Problem #3. X is a random variable with an exponential
distribution with rate λ = 7 Thus the pdf of X is f(x) = λ
e−λx for 0 ≤ x where λ = 7.
a) Using the f(x) above and the R integrate function calculate the
expected value of X.
b) Using the f(x) above and the R integrate function calculate the
expected value of X2
c) Using the dexp function and the R integrate command calculate
the expected value...

X be random variable with distribution negative
binomial NB(p,r) . r is known, 0<p<1 unknown. Find the UMVUE
of log (p)

6. A continuous random variable X has probability density
function
f(x) =
0 if x< 0
x/4 if 0 < or = x< 2
1/2 if 2 < or = x< 3
0 if x> or = 3
(a) Find P(X<1)
(b) Find P(X<2.5)
(c) Find the cumulative distribution function F(x) = P(X< or
= x). Be sure to define the function for all real numbers x. (Hint:
The cdf will involve four pieces, depending on an interval/range
for x....

Suppose that the random variable X has the following cumulative
probability distribution
X: 0 1. 2. 3. 4
F(X): 0.1 0.29. 0.49. 0.8. 1.0
Part 1: Find P open parentheses 1 less or equal than
x less or equal than 2 close parentheses
Part 2: Determine the density function f(x).
Part 3: Find E(X).
Part 4: Find Var(X).
Part 5: Suppose Y = 2X - 3, for all of X, determine
E(Y) and Var(Y)

Part II
Suppose the discrete random variable X has the
following probability distribution.
x
-2
0
2
4
6
P(X=x)
0.09
0.24
0.33
a
0.14
Find the value of a so that
this probability distribution is valid. (Sec. 4.3)
(Sec. 4.4)
Find the mean of the random variable X in Exercise 1
above.
Find the variance of the random variable X in Exercise
1 above.
Consider the following table for the number of automobiles in
Canada in 2005 by vehicle...

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