- 1 In A Rectangle Abcd A 0 B N N C 1 0 D 0 0 The Two Dimensional Probability Density Function Of The Random 1 (51.26 KiB) Viewed 12 times
1. In a rectangle ABCD: A(0,-), B(n,-n), C(1, 0), D(0,0) the two-dimensional probability density function of the random variable (X,Y) is p(x, y) = cx cos² (x + y) and is equal to zero elsewhere. Calculate: a. The unknown parameter c; b. Find the probability density functions of the components X and Y and plot them; c. The conditional probability density functions of the components; d. Find the conditional mean values; e. The value of the distribution function F(π/2, -1/4); f. The probability P(X> n/3 and Y> -π/2). 2. There is a given sample X on a data file (choose column B). a. Show a table of an automatic interval statistical frequency distribution of 12 intervals; b. Draw a polygon of this interval statistical frequency distribution of 12 intervals; c. Find these empirical values: expected value, variance, standard deviation; d. Write down which value or values could be considered as the mode of the interval distribution; e. Check the hypothesis that data X is normally distributed with some chosen parameters, rounded from the ones that were got on c).