0. Calculate the parameter a as the sum of the last three digits of your index number, modulo 6 (remainder after division by 6): a = (di + d2+ d3) mod 6 1. Joint Probability Mass Function (PMF) of a random vector (X,Y) is given by the following table: 10. (a + 1) 0 20. (a + 1) X/Y -(a + 1) 0 1/30 1/15 1/20 1/10 1/10 1/5 1/60 1/30 3/20 1/15 ? 5. (a + 1) 10. (a + 1) 2/15 Using programming language Python: a. (1 point) Find the missing element. b. (10) Find (marginal) PMFs of RVs X and Y. C. (1p) Check whether RVs X and Y are independent. d. (2p) Find mathematical expectations, variances, covariance and correlation coefficient of RVs X and Y. e. (2p) Find third quartile (quantile of order 0.75) of RV X. f. (2p) Change elements in the third row of the joint distribution (corresponding to X = 5. (a + RVs X and Y become independent. WhatsApp 0. Calculate the parameter a as the sum of the last three digits of your index number, modulo 6 (remainder after division by 6): a = (di + d2+ d3) mod 6 1. Joint Probability Mass Function (PMF) of a random vector (X,Y) is given by the following table: 10. (a + 1) 0 20. (a + 1) X/Y -(a + 1) 0 1/30 1/15 1/20 1/10 1/10 1/5 1/60 1/30 3/20 1/15 ? 5. (a + 1) 10. (a + 1) 2/15 Using programming language Python: a. (1 point) Find the missing element. b. (10) Find (marginal) PMFs of RVs X and Y. C. (1p) Check whether RVs X and Y are independent. d. (2p) Find mathematical expectations, variances, covariance and correlation coefficient of RVs X and Y. e. (2p) Find third quartile (quantile of order 0.75) of RV X. f. (2p) Change elements in the third row of the joint distribution (corresponding to X = 5. (a + RVs X and Y become independent. WhatsApp