Question

Part 1. Random Events probability of some event in each experiment is o.009. Find the probability of exactly 3 square has a side of 21 cm and has a circle with radius equal to 7 cm within it. Find the of people attend their primary care physician regularly: 28% of those people have no 1. The successes during 340 experiments. 2. A probability of a dart hitting the circle if it hits the square 3.75% health problems crop up during the following year. Out of the 25% of people who don't see their doctor regularly, only 18% have no health issues during the following year. What is the probability a random person will have no health problems in the following year? Part 2. Random Variables 4. Let X be a continuous random variable with probability density function: 0, x<1 if (x2 +1), if 1 sxs 4 24 if x 4 0 Find the standard deviation of random variable X.

Answer 1

Probability = 0.009 = event success probability of r occurrence during n experiments with success probability = p and failure probability = q (p + q = 1) is n_c_r p^r q^n-r Here p = 0.009 q = 0.991 r = 3 n = 340 Therefore probability = 340_c_3 (0.009)^3 (0.991)^337 = 340 times 339 times 338/6 times (0.009)^3 (0.991)^337 = 0.2249 square side = l_s = 21 cm circle radius = r_c = 7 c m let s be random variable representing square let c be random variable representing circle subset subset S equivalent C is inside s p(S union C) = p(s) p(s intersection c) = p(c) Here, p(s) and p(c) are area of square and circle respectively. Probability of dart hitting circle if it hits the square is = p(c/s) = p(c intersection s)/p(s) = p /p(s) = pi r^2_c/l^2_s = pi times 7^2/21^2 9 = pi/9 = 0.3491.