Question: 6. Let X be a continuous random variable with density and distribution functions f and F, respectively. Assuming that R is a point

6. Let X be a continuous random variable with density and distribution functions f and F, respectively. Assuming that α ∈ R is a point at which P (X ≤ α) < 1, prove that h(x) =    f (x) 1 − F (α) if x ≥ α 0 if x < α is also a probability density function.

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 Probability And Stochastic Modeling Questions!

2.1 Marginal and conditional probability: The social mobility data from Sec- tion 2.5 gives a joint probability distribution on (Y1, Y2)= (father's oc- cupation, son's occupation). Using this joint...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

re Regular Languages and Finite Automata (a) Let L be the set of all strings over the alphabet {a, b} that end in a and do not contain the substring bb. Describe a deterministic finite automaton...

4. Let X be the number of major storms in a particular state in a given year. The probability of having no major storms is 0.50, of one major storm is 0.30, of two major storms is 0.10, of three...

i just need to solve part 1 please Part 1 Consider a network that has four nodes n1, n2, n3 and n4, and six directed arcs of the form a1 = (n1, n2), a2 = (n1, n3), a3 = (n2, n3 ), a4 = (n3), n2), a5...

6. Let X be a continuous random variable with probability density function f (x ) = be-bx, x>0 ; b>0 elsewhere Find the moment generating function of X, Mx (t) . Then, find M x (-6b). 7. Let X be a...

Let X be a continuous random variable with density function f (x), x RX, and distribution function F(t), t . Express the density function and the distribution function of the random variable Y = X2...

1. Consider a network that has four nodes n1, n2, n3 and n4, and six directed arcs of the form a1 = (n1, n2), a2 = (n1, n3), a3 = (n2, n3 ), a4 = (n3), n2), a5 = (n2, n4) and a6 = (n3, n4), where the...

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...

The table provides the ages of all 50 heads of households in a small Nova Scotian fishing village. The distribution of these ages is characterized by = 47.18 and = 14.74. a. Find the mean of the...

Healthy Foods just paid its annual dividend of $1.62 a share. The firm recently announced that all future dividends will be increased by 2.1 percent annually. What is one share of this stock worth to...

The use of stock as a meaningful portion of a transaction generally leads to a: Question 16 options: A) Higher valuation B) Lower valuation C) Higher multiple D) It depends

Draw all constitutional isomers with molecular formula C 4 H 11 N, and provide a name for each isomer.