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YOUR TURN 1 Repeat Example 1 for the probability density function
EXAMPLE 1 Expected Value and Variance
Find the expected value and variance of the random variable
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Chapter 13 Solutions
Calculus For The Life Sciences
- What is the variance of a continuous random variable X whose probability density isarrow_forwardProve that fx is a true probability function, find its value expected and its variance.arrow_forwardIf a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!arrow_forward
- If the probability density function of the random variable p(1-p)*-1 if x=1,2,3,....,0 otherwise then the expected value of X equal P/1arrow_forwardJust a quick question for a derived random variable, how do you know that f(m) = f(x) abs(dx/dm)? Is that a theorem?arrow_forwardHelp me with this homework question please question 2arrow_forward
- The random variable x follows a uniform probability distribution in the interval (0,1); the probability of obtaining x values outside this range is zero. What is the probability distribution of y = ln x?arrow_forwardA random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x– x² +4) =arrow_forwardLet ZZ be a discrete random variable taking one of the four distributions covered in Chapter 10. Suppose you know that Var(Z)=(k+1)E(Z)Var(Z)=(k+1)E(Z) where kk is the last non-zero digit of your student ID number. Determine the distribution of ZZ and find its parameter(s), explaining your argument carefully.arrow_forward
- Q.1 The probability mass function for a discrete random variable X is defined as ((1+0)" (^) 0x; x = 0, 1, 2, 3, ..., n fx(x) = {(1 + 0; e. w. where > 0. Show that it is probability mass function. Find its mean and variance.arrow_forwardQuestion 1.2 Consider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise) Calculate P (x = 3) Calculate P (2 < or = x < or = 3) Question 1.3 Consider the function f (x) = (k - x/4 1 < or = x < or = 3) = (0 otherwise) which is being used as a probability density function for a continuous random variable x? a. Find the value of K b. Find P (x < or = 2.5)arrow_forwardPlease don't copyarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
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