Question

Examination in probability theory and statistics Variant 9 1. Discrete distribution for X is given by the following table: Probability p ValueX Find distribution function fa) and median Me(0). Calculate mathematical expectation (the mean) M(x), 0.3 -10 0.4 10 0.2 20 0.1 40 variance (dispersion) Da, standard error ơ(X), asymmetry coefficient As(X) and excess Ex(X). 2. Calculate multiplier k. Find mode Mots, median Me(o), mathematical expectation (the mean) Mc) variance (dispersion) D(x) and standard error σ(x) for continuous distributions having the give probability densities a) b) p(x) =t(20x-x2) 0 x 20 Find distribution function f(x) and x<0 (x-9) 277 x > 20 Find asymmetry coefficient As() and excess Exfa) calculate probability that x e|-5,10] 3. A box contains lotto cards: 5 cards are with letters, 3 are with numbers, and 2 are with pictures. have taken 2 cards from the box. What are probabilities that we have taken a) 2 cards with pictures c) card with letter and card with number b) at least one card with picture d) no cards with numbers

Answer 1