Answered: QUESTION 2 a) Suppose that random… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

See similar textbooks

Related questions

Question

QUESTION 2
a) Suppose that random variables X₁ and X₂ have exponential distribution with expected value of
and respectively. Assume that X₁ and X₂ are independent of each other.
Find
i) The joint density function of X₁ and X2.
ii) P(X₂ >1, X₂ > 1)
iii) P(X₂ <5)
b) A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in
years is given by
f(y) =
100
0<y<∞
elsewhere
0,
Derive the expected value of Y?

Expert Solution

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

If the random variable T is the time to failure of a commercial product and the values of its probability den-sity and distribution function at time t are f(t) and F(t), then its failure rate at time t is given by f(t)1 − F(t). Thus, thefailure rate at time t is the probability density of failure attime t given that failure does not occur prior to time t.(a) Show that if T has an exponential distribution, thefailure rate is constant. (b) Show that if T has a Weibull distribution (see Exer-cise 23), the failure rate is given by αβt β−1.
Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?
- If we assume that the moment of death of a tilapia fish in one of the commercial ponds for selling fish is Random and regular on the time period [300,0] where time is measured in minutes. So what is it Prospect 1. That the moment of death of this fish is more than three hours 2- This fish should live less than three hours 3- Find the density function, then find the expectation and variance
Suppose that Y1, . . . , Yn is a random sample from a population whose density function is
1(a)Consider the random variable model with density function given byf(x)= { 2kx/45, 0≤x≤5 2k(30−x)/45 , 5≤x≤10 0, otherwise Compute the(i) expected value(ii) standard deviation.comment and discuss on the output of these two components with the type the random variable model defined (b). If f (x)=ce−0.2x , if 0≤x≤10 and 0, otherwiseBased on your computations below, explain and discuss the variousprobabilities with respect to the given exponential function.(i)deduce the constant c, (ii)compute the probabilities(alpha) p(x≥5) (beta) p(x<4) (gamma) p(3≤x≤11)
If two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS