Just a regular student: Alex, your friend and a hard-working student with an xiety is enrolled in a probability course. Raised in a perfectionist background, he is worried about quizzes messing up his grade. Each quiz is out of 5 marks and due to Alex's hard work you know that his score on each quiz can be modelled by a Uniform random variable X distributed on the interval [3.5, 5] and you know that his performance on each quiz is independent from other quizzes. The course has 12 quizzes and it is n- 2. Alex comes to you to comfort him and help him revise concepts. You decide to do both at the same time. 5. (a) What is the probability that he will score less than 4 in a particular quiz. (b) Write the CDF for X. (c) What is the expec ted score (out of 50) if he gives only the first 10 quizzes. (d) he is satisfied with each quiz that is counted. (Meaning he has > 4 in at least 10 quizzes). Alex is satisfied with a quiz, if he gains at least 4 in each quiz. What is the probability that (e) his scores vary. What is the stand ard deviation for each quiz? Your friend is now comforted and goes for a break. You wonder to yourself, how much will

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.