Question

**10.** Times between accidents are i.i.d.
exponential with mean 2. The fourth accident triggers an alarm.
Find the density function of the time of this alarm.

Answer #1

Problem 10. Times between accidents are
identically independently distributed exponential with mean 2. The
fourth accident triggers an alarm. Find the density function of the
time of this alarm.

Assume that the time between two consecutive accidents in a
chemistry lab follows an exponential distribution with parameter 入.
Starting to count from the day of the first accident (this will be
day 0), there has been accidents on the 28th, 50th, 60th
days. Compute the maximum likelihood estimate of 入. Explain the
steps.

X and Y ar i.i.d. exponential random variables
with mean = 2. Let Z = X + Y. The
probability that Z is less than or equal to 3 is:

Customers arrive at
random times, with an exponential distribution for the time between
arrivals. Currently the mean time between customers is 6.34
minutes. a. Since the last customer arrived, 3 minutes have gone
by. Find the mean time until the next customer arrives.
b. Since the last
customer arrived, 10 minutes have gone by. Find the mean time until
the next customer arrives.

Let X be an Exponential random variable with mean 1. Find the
density function for Y = {X}^0.5. Evaluate the density function (to
2 d.p.) of Y at the value 1.4.

1
Let X be an accident count that follows the Poisson distribution
with parameter of 3.
Determine:
a
E(X)
b
Var(X)
c
the probability of zero accidents in the next 5 time periods
d
the probability that the time until the next accident exceeds n
e
the density function for T, where T is the time until the next
accident
2
You draw 5 times from U(0,1). Determine the density function for...

STAT 180 Let X and Y be independent exponential random variables
with mean equals to 4.
1) What is the covariance between XY and X.
2) Let Z = max ( X, Y). Find the Probability Density Function
(PDF) of Z.
3) Use the answer in part 2 to compute the E(Z).

A safety engineer claims that all rush hour automobile
accidents are uniformly distributed between 2:30 pm and 5:15 pm.
Assume that this is correct and find the probability of car getting
into a rush hour accident between 3:48 pm and 4:07 pm.

The time between wildfires in Santa Barbara County follow an
exponential distribution with a mean time of 3 months (or 0.25
years). Find the probability that the time between wildfires in
Santa Barbara County is between 3 and 5 months.

The time between arrivals at a toll booth follows an
exponential distribution with a mean time between arrivals of 2
minutes.
What is the probability that the time between two successive
arrivals will be less than 3 minutes?
What is the probability that the time will be between 3 and 1
minutes?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 12 minutes ago

asked 13 minutes ago

asked 19 minutes ago

asked 19 minutes ago

asked 32 minutes ago

asked 34 minutes ago

asked 42 minutes ago

asked 44 minutes ago

asked 47 minutes ago

asked 51 minutes ago

asked 51 minutes ago