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Suppose you have an innitely large bag of M&M's and you only like to eat blue M&M's. Suppose furthermore that you pick a blue M&M with probability p = 0.1. i) What is the probability mass function of the random variable that corresponds to picking a blue M&M after having selected 14: 2 0 times another color? Do not forget to provide the support. ii) How do we call a random variable X with this pmf'? iii) Derive lE[X] and calculate its value. iv) What is the probability that you did not pick a blue M&M in the rst three attempts? v) Given that you did not pick a blue M&M in the rst ve attempts, what is the probability that you will not pick a blue M&M in the next three attempts? vi) Compare and interpret your answers to question iv) and question v)