Purchase Solution

Probability density function

Not what you're looking for?

Ask Custom Question

4. The probability density function if X, the lifetime of a certain type of electronic device (measured in hours} is given by:
f(x) =
10/x^2 for x>10
and
=0 for x<=10

(a) Find P {X > 20}
(b) What is the cumulative distribution function of X?
(c) What is the probability that of 6 such types of devices at least 3 will function for at least 15 hours? What assumptions are you making?

{see attachment}

Attachments
Purchase this Solution
Solution Summary

The expert finds probability, cumulative distribution function.

Solution Preview

See attached file

(This problem is from Continuous Random Variables.)

a) P { X>20}

f (x) = 10/ x2
P (X>20) = ∫ f(x) dx = ∫10/ x2 dx with the limits 20 and infinity
= ∫10/ x2 dx = -10 /x
calculating the integral within the limits 20 and infinity
= [- 10 / x ] 20 ∞

= - 10 ( 1 / ∞ - 1/20 ] = - 10 ( 0 - 0.05 ) = 10 * 0.05 = 0.5
Answer: P { X>20}= 0.5

b) cumulative distribution function of X

F (x) = cumulative distribution function of X = ∫ f(x) dx = ∫10/ x2 dx calculated ...

Purchase this Solution
Free BrainMass Quizzes
Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

View More Free Quizzes
Related BrainMass Solutions

  • Probability and Probability Density

    Definition of probability density function: The probability density function is a function of a random variable on a given domain. At each given point of a random variable, the probability density function is a probability.

  • Statistics: Probability density function, central limit theorem

    Thus the probability density function of is given by d) We have the probability density function of as: (1) Let .

  • Exponential probability density function

    This solution includes calculations involving exponential probability density function.

  • Finding the Probability Density Function

    We can find the probability mass function for Y. 1) When 2) When 3) When 4) When So, the probability density function of Y=10X-4 is The expert finds the probability density functions.

  • Density Functions: Time takes students to finish aptitude test

    Thus the probability density function is . b) The plot of the density function is given below. c) The cumulative distribution function of the random variable is given by, .

  • Probability: continous random variable

    Then the distributive function of is Then the probability density function of is Therefore, we have Using brief, step by step calculations in an attached Word document, this solution proves the probability density function.

  • Probability density function

    10719 Probability density function ) Let X and Y have joint probability density function f(x,y) (s,t) = ce ^ -(s + 2t) for 0 <= s, and 0 <= t.

  • Probability density function

    192253 Probability Density Function: Determine the Probability Problem attached. Suppose that a random variable X has a probability density function f(x)=Ce^-2x....

  • Probability density function

    31289 Probability density function #39. If X is an exponential random variable with parameter λ = 1, compute the probability density function of the random variable Y defined by Y = log X. #40.

  • Probability Density Function

    20004 Probability density function Assume that X is a random variable with a probability density function f(x)=cx^2, -1probability density function is

View More Related Solutions