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Start with the joint distribution of treatment group and response in Table 3.6 on page 138. For each treatment group, compute the conditional distribution of response given the treatment group. Do they appear to be very similar or quite different?

Short Answer

Expert verified

The fourth one looks quite different from the others, especially from the second.

Step by step solution

01

Given information

Referring to the Table 3.6.

02

Necessary calculation

There are four different treatments on which conditional distribution.

The marginal p.d.f. of treatment Y is given in the bottom row of the referring table in the text.

The conditional p.d.f. of the response given each treatment is the ratio of the two rows above that to the bottom row.

\({g_1}\left( {x\left| 1 \right.} \right) = \left\{ {\begin{array}{*{20}{c}}{\frac{{0.120}}{{0.267}} = 0.449438}&{if\,x = 0}\\{\frac{{0.147}}{{0.267}} = 0.550562}&{if\,x = 1}\end{array}} \right.\)

\({g_1}\left( {x\left| 2 \right.} \right) = \left\{ {\begin{array}{*{20}{c}}{\frac{{0.087}}{{0.253}} = 0.343874}&{if\,x = 0}\\{\frac{{0.166}}{{0.253}} = 0.656126}&{if\,x = 1}\end{array}} \right.\)

\({g_1}\left( {x\left| 3 \right.} \right) = \left\{ {\begin{array}{*{20}{c}}{\frac{{0.146}}{{0.253}} = 0.577075}&{if\,x = 0}\\{\frac{{0.107}}{{0.253}} = 0.422925}&{if\,x = 1}\end{array}} \right.\)

\({g_1}\left( {x\left| 4 \right.} \right) = \left\{ {\begin{array}{*{20}{c}}{\frac{{0.160}}{{0.227}} = 0.704846}&{if\,x = 0}\\{\frac{{0.067}}{{0.227}} = 0.295154}&{if\,x = 1}\end{array}} \right.\)

Therefore, the fourth one looks quite different from the others, especially from the second.

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