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Chapter 3: Q14E (page 117)

Find the quartiles and the median of the binomial distribution with parametersn=10 andp=0.2.

Short Answer

Expert verified

The median of the distribution is 0.268.

The quartiles of the distribution are


Step by step solution

01

Given information

Given the binomial distribution of the parameter is n=10 andp=0.2.

02

State the distribution

03

Compute the quantile function and median

Then by tabulating the values of cdf and pdf is

Then the quantiles values are given by

Hence the median is 0.268.

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Most popular questions from this chapter

Question:Suppose thatXandYhave a continuous joint distribution for which the joint p.d.f. is

\({\bf{f}}\left( {{\bf{x,y}}} \right){\bf{ = }}\left\{ \begin{array}{l}{\bf{k}}\;{\bf{for}}\;{\bf{a}} \le {\bf{x}} \le {\bf{b}}\;{\bf{and}}\;{\bf{c}} \le {\bf{y}} \le {\bf{d}}\\{\bf{0}}\;{\bf{otherwise}}\end{array} \right.\)

wherea <b,c < d, andk >0.

Find the marginal distributions ofXandY.

Suppose that the joint distribution of X and Y is uniform over a set A in the xy-plane. For which of the following sets A are X and Y independent?

a. A circle with a radius of 1 and with its center at the origin

b. A circle with a radius of 1 and with its center at the point (3,5)

c. A square with vertices at the four points (1,1), (1,鈭�1), (鈭�1,鈭�1), and (鈭�1,1)

d. A rectangle with vertices at the four points (0,0), (0,3), (1,3), and (1,0)

e. A square with vertices at the four points (0,0), (1,1),(0,2), and (鈭�1,1)

Let X1鈥�,Xn be independent random variables, and let W be a random variable such that \({\rm P}\left( {w = c} \right) = 1\) for some constant c. Prove that \({x_1},....,{x_n}\)they are conditionally independent given W = c.

Return to the situation described in Example 3.7.18. Let\(x = \left( {{x_1},.....,{x_5}} \right)\)and compute the conditional pdf of Z given X = x directly in one step, as if all of X were observed at the same time.

Suppose that \({{\bf{X}}_{\bf{1}}}\;{\bf{and}}\;{{\bf{X}}_{\bf{2}}}\) are i.i.d. random variables andthat each of them has a uniform distribution on theinterval [0, 1]. Find the p.d.f. of\({\bf{Y = }}{{\bf{X}}_{\bf{1}}}{\bf{ + }}{{\bf{X}}_{\bf{2}}}\).
See all solutions

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