let X be a geometric random variable, representing the number of trails up until first heads occurs.
so, $X=4$ will represent the event $T_1T_2T_3H_4$
part a
given this information, why would $X-1=3$ represent the event $T_2T_3H_4$?
isn't $X-1=3$ same as $X=4$? so, by that logic shouldn't they represent the same event?
what event would $aX-b$ represent?
part b
assuming the parameter for X is p, how can $P(X=k,X>1)$ be represented in terms of p and k.
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abhishek
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I'm not sure what you are asking. The question reads like it was copied directly from an assignment. Or are you saying, in part a, that the answer given is $T_2T_3H_4$ and you question why that is correct? – saulspatz Oct 05 '18 at 14:59
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it is from a lecture video.the instructor uses part a to explain memorylessness of geometric random variables.and part b to explain variance of geometric random variables – abhishek Oct 05 '18 at 15:26
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yes you are correct. – abhishek Oct 05 '18 at 15:27
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link to video lecture. https://courses.edx.org/courses/course-v1:MITx+6.431x+3T2018/jump_to/block-v1:MITx+6.431x+3T2018+type@vertical+block@ch6-s3-tab10 – abhishek Oct 05 '18 at 15:36