Question: If Y is a continuous variable with density function f(Y) that is symmetric about 0, that is, f(y) = f(y) for all y, and E(Y)

If Y is a continuous variable with density function f(Y) that is symmetric about 0, that is, f(y) = f(y) for all y, and E(Y) exists.

Show that E(Y) = 0.

Hint:

E(Y) =

yf(y)dy=0yf(y)dy+0yf(y)dy

Make the change of variable x=-y in the first integral.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

7. Let X be a continuous random variable with density function f . We say that X is symmetric about if for all x, P (X + x) = P (X x). (a) Prove thatX is symmetric about if and only if for all...

Q:

Let X be a continuous random variable with density function f . We say that X has a symmetric distribution around the point a if we have P(X a + x) = P(X a x) for any x . (i) Show that the...

Q:

This exercise will lead you through a proof of Chebyshevs inequality. Let X be a continuous random variable with probability density function f (x). Suppose that P(X

Q:

15. Let X be a continuous random variable with density function f . A number t is said to be the median of X if P (X t) = P (X t) = 1 2 . By Exercise 7, Section 6.1, X is symmetric about if and...

Q:

Assume that X is a continuous random variable with density function f and distribution function F. Suppose that a is a real number for which P(X a) Show that the function h defined by is also a...

Q:

Hello I need your help please about Variance 1- Can we have a random variable X with E( X ) = 3 and E( X 2 ) = 8? 2- Let X be a random variable with density function f ( x ) = 1 + x for 1 x 0, f ( x...

Q:

Suppose that the time (in hours) it takes to repair a certain car part is a continuous random variable with the density function f ( x)=0.75e ?0.75 x for x > 0 (and f(x) = 0 otherwise). a) Verify...

Q:

solve this question Problem 3 Let X1. .... X, be independent and identically distributed continuous random variables with a positive continuous joint probability density function f(x1. . . ., X'n)....

Q:

Problem 3 Let X1. .... X, be independent and identically distributed continuous random variables with a positive continuous joint probability density function f(x1. . . ., X'n). 3pts (i) Suppose that...

Q:

f a processor exhibited one branch delay slot how would you reorder (and possibly modify) the instructions in the following loop to gain a performance advantage? loop ldr r2,r3,#4 % r2=load(r3),...

Q:

An astronaut on a strange planet finds that she can jump a maximum horizontal distance of 15.0 m if her initial speed is 3.00 m/s. What is the free-fall acceleration on the planet?

Q:

Find the slit separation of a double-slit arrangement that will produce interference fringes 0.018 rad apart on a distant screen when the light has wavelength = 589 nm.

Q:

Discuss the three diff"erent procedures that a company's management might follow to set profit objectives. 4 The classical economic model of competition assumes that the objective of ' the...

Q:

2. Age 30. Retire at age 65. Expected retirement term of 17 years. $32,000 salary now, expected to grow by 1.5% per year. Defined benefit formula = final year's salary x # years worked x.01. Assume...

Q:

3. Assess the quality or value of communication by examining its six characteristics

Q:

5. Describe the visual representations, or models, of communication

Q:

4. Define what communication scholars consider to be competent communication