Suppose it is known that the life X of a particular compressor, in hours,has the density function( )/9001 , 0,9000,xe xf xotherwise− = a. Find the mean life of the compressor.b. Find2X .c. Find the variance and standard deviation of the random variable X
Question
Suppose it is known that the life X of a particular compressor, in hours,has the density function( )/9001 , 0,9000,xe xf xotherwise− = a. Find the mean life of the compressor.b. Find2X .c. Find the variance and standard deviation of the random variable X
Solution
The question seems to be about the properties of a random variable with a given probability density function (pdf). However, the pdf is not clearly stated. Could you please provide the correct pdf?
Generally, for a continuous random variable X with pdf f(x), the mean (or expected value) E[X] is given by the integral of x*f(x) over the range of X.
The expectation of X^2, E[X^2], is given by the integral of x^2*f(x) over the range of X.
The variance Var(X) is given by E[X^2] - (E[X])^2, and the standard deviation is the square root of the variance.
Once you provide the correct pdf, we can proceed with the calculations.
Similar Questions
Assume the length X, in minutes, of a particular type of telephoneconversation is a random variable with probability density function( )/51 , 0,50,xe xf xotherwise− = a. Determine the mean length X of this type of telephoneconversation.b. Find the variance and standard deviation of X
Suppose a random variable X has the following probability density function: Find standard deviation, ? (Hint :first find the value of A so that is a probability density function and then calculate standard deviation).
Suppose a manufacturer wants to estimate the averagelifespan of a new product they have developed. Theyrandomly select 15 products and test them until they fail.It is known that the average lifespan is 120 hours, with astandard deviation of 10 hours. Assume that the lifespanof the products follows a normal distribution. Themanufacturer wants to know the probability that theaverage lifespan of the product is greater than 130 hours.
Suppose that the lifetimes of old-fashioned TV tubes are normally distributed with a standard deviation of 1.2 years. Suppose also that exactly 35% of the TV tubes die before 4.5 years. Find the mean lifetime of TV tubes. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
Qn.2. (a) A continuous random variable x has the pdf, f(x) = 2 xk 0< x < 1 and 0 otherwise find the (i) value of the constant k (ii) mean and standard deviation of X (b) A random variable X takes on the integer value x, with probability, Q (X= x) such that, Q(X= x) = k x3, for x = 1,2,3,4 and 0 otherwise Find (i) value of k (ii)Mean and variance of the distribution (iii) Mean and variance of 2X- 4
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.