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An urn contains 3 white and 6 red balls. Four balls are drawn one by onewith replacement from the urn. Find the probability distribution of the number of red ballsdrawn. Also find mean and variance of the distribution. |
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Answer» There are total 9 balls Success:drawing a red ball. `n=4,P=6/9=2/3,q=1/3` P(r red balls)=P(X=r) `=nC_rP^rQ^(n-r)=4C_r(2/3)^r(1/3)^(4-r)` `=4C_r*2^r/3^4` Mean=`sumx_iP_i` `=0+8/81+(2*24)/81+(3*32)/81+(4*16)/81` `=(0+8+48+96+64)/81=2.66` Variance=`sumx_i^2P(x=x_i)-mu^2` `=(0+8+96+288+256-276)/81` `=124/27`. |
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