At the start of a cricket match, a coin is tossed and the team winning the toss has the opportunity to choose to bat or bowl. Such a coin is unbiased with equal probabilities of getting head and tail.

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CASE_STUDIESProbability Distribution of a Random VariableBernoulli Trials in ProbabilityCBSE PYQ2 sub-questions

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A pair of dice is thrown simultaneously. If X denotes the absolute difference of the numbers appearing on top of the dice, then find the probability distribution of X.

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Self-study helps students to build confidence in learning. It boosts the self-esteem of the learners. Recent surveys suggested that close to 50% learners were self-taught using internet resources and upskilled themselves. A student may spend 1 hour to 6 hours in a day in upskilling self. The probability distribution of the number of hours spent by a student is given below : P(X = x) = {kx², for x = 1, 2, 3; 2kx, for x = 4, 5, 6; 0, otherwise} where x denotes the number of hours. Based on the above information, answer the following questions :

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