Geometric Distribution. (Discrete waiting time distribution) It is known that 1% of bits transmitted through a digital transmiss
ion are received in error. Bits are transmitted until the first error. Let X be the number of transmitted bits including the first error. a. What are the possible values of X? (Support) b. What is the pmf of X? C. Show that P(X>t+s|X>t) is independent of t, where s and t are positive integers. (Memoryless) d. What is the mean of X? You can either derive it, or show it with R. simulations.
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Points of inflections are zeroes of the second derivative. We have:
So, the second derivative equals zero if and only if
So, this is the only point of inflection of this function.