Let's now look at the binomial test for the 50% hypothesis for the girls In fact, 7 girls liked the cake and 1 didn't That's a pretty extreme result for a 50% probability Is it actually compatible with a true population probability of 50%? Expected girls from one couple$ {}=0.5\cdot1 + 0.25\cdot1 =0.75$ expected boys from one couple$ {}=0.25\cdot1 + 0.25\cdot2 =0.75$ 1 as i said this works for any reasonable rule that could exist in the real world An unreasonable rule would be one in which the expected children per couple was infinite.
A couple decides to keep having children until they have the same number of boys and girls, and then stop Assume they never have twins, that the trials are independent with probability 1/2 of a boy, and that they are fertile enough to keep producing children indefinitely. 1st 2nd boy girl boy seen boy boy boy seen girl boy the net effect is that even if i don't know which one is definitely a boy, the other child can only be a girl or a boy and that is always and only a 1/2 probability (ignoring any biological weighting that girls may represent 51% of births or whatever the reality is). A couple decides to keep having children until they have at least one boy and at least one girl, and then stop Assume they never have twi. 3 given that boys' heights are distributed normally $\mathcal {n} (68$ inches, $4.5$ inches$)$ and girls are distributed $\mathcal {n} (62$ inches, $3.2$ inches$)$, what is the probability that a girl chosen at random is taller than a boy chosen at random?
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