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Chapter 3: Q5E (page 116)

Suppose that the c.d.f. of a random variable X is as

follows:


Find and sketch the p.d.f. of X

Short Answer

Expert verified

The c.d.f. of a random variable is as follows:


Step by step solution

01

Given information

The c.d.f. of a random variable is as follows:


02

calculate the PDF

03

Sketch the PDF

In the graph, the x-axis denotes the random variable X and the y-axis denotes the corresponding PDF of X. For example, for X =1 corresponding PDF is 2/9S.

Plotting PDF of random variable X for every value of X, a PDF curve is obtained.

Then the PDF curve is given by

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Most popular questions from this chapter

Suppose that a coin is tossed repeatedly in such a way that heads and tails are equally likely to appear on any given toss and that all tosses are independent, with the following exception: Whenever either three heads or three tails have been obtained on three successive tosses, then the outcome of the next toss is always of the opposite type. At time\(n\left( {n \ge 3} \right)\)let the state of this process be specified by the outcomes on tosses\(n - 2\),\(n - 1\)and n. Show that this process is a Markov chain with stationary transition probabilities and construct the transition matrix.

Let the initial probability vector in Example 3.10.6 be\(v = \left( {\frac{1}{{16}},\frac{1}{4},\frac{1}{8},\frac{1}{4},\frac{1}{4},\frac{1}{{16}}} \right)\)Find the probabilities of the six states after one generation.

Suppose that the p.d.f. of a random variable X is as follows:

\(f\left( x \right) = \left\{ \begin{array}{l}3{x^2}\,\,for\,0 < x < 1\\0\,\,otherwise\end{array} \right.\)

Also, suppose that\(Y = 1 - {X^2}\) . Determine the p.d.f. of Y

Suppose that thenrandom variablesX1, . . . , Xnform a random sample from a continuous distribution for which the p.d.f. isf. Determine the probability that at leastk of thesenrandom variables will lie in a specified intervala≤x≤b.

If 10 percent of the balls in a certain box are red, and if 20 balls are selected from the box at random, with replacement, what is the probability that more than three red balls will be obtained?
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