Binomial / Geometric Distributions - S1 -

I'm not really sure on any of this question and quite confused on it. Would really appreciate help on this please.

For a) i ) , how would you know that the mean is equal to the median ? The median would be the space thats right in the middle ? So it will have 2 same height bars ?

For b) i ) Don't know what to do.

ii and iii ) ...........

Reply 1

dknt

12

Original post by WildBerry

I'm not really sure on any of this question and quite confused on it. Would really appreciate help on this please.

For a) i ) , how would you know that the mean is equal to the median ? The median would be the space thats right in the middle ? So it will have 2 same height bars ?

For b) i ) Don't know what to do.

ii and iii ) ...........

Not 100% with part i), but for a), look out for symmetry in the graphs. This way the mean will be in the middle, with the median.

b) Look for graphs with a skew. If it is skewed to the right, the mean goes higher. If the graph is skewed left, then then mean becomes lower.

ii) Think about how geometric distribution probabilities are calculated... for X=1, we have p, for 2 we have p(1-p), then p(1-p)^2, then p(1-p)^3... given that probabilities are always fractional (excluding 1 and 0), which probability will always be the largest and what happens to the probabilities as X=1,2,3,4,5, etc.

iii) Again think about the values of the probabilities in a binomial distribution. For a given number of trials, there will always be a certain number of trials which will most be most likely to occur.

Reply 2

WildBerry

OP

a) Thanks, I got the part a right now .

b ) Still not sure with part b , aren't they all skewed positively / the same ?

ii ) Will the probability always decrease as you go more higher ? Because each one becomes raised to a power as you go higher so it gets lower when you times it out ?

iii) Can you give an example of a binomial distribution where that is the case ? I can't really think of one where one specific trial will have one most likely outcome ?

Reply 3

dknt

12

Original post by WildBerry

a) Thanks, I got the part a right now .

b ) Still not sure with part b , aren't they all skewed positively / the same ?

ii ) Will the probability always decrease as you go more higher ? Because each one becomes raised to a power as you go higher so it gets lower when you times it out ?

iii) Can you give an example of a binomial distribution where that is the case ? I can't really think of one where one specific trial will have one most likely outcome ?

for b), consider the 2nd graph. Can you see that it is skewed towards the right? Similarly, for the last graph, it is skewed towards the left. If you cant see it try drawing a smooth line above the tops of the bars.

ii)Yes so you start with the maximum value of p, and it will decrease. Do any of the graphs show that?

iii)It's not that one specific trial will be more likely to occur, just a group of trials. Consider X~B(10, 0.5), it is most likely that out of the 10 trials you will succeed 5 times, so on a graph you could get a peak at 5. Similarly, Y~B(40, 0.25), it would be most likely we would get 10 successes. With this is mind would there ever be a case where you'd get 2 sets of trails that would be most likely (i.e. Bi-modal)?

Binomial / Geometric Distributions - S1 -

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