Number of valence

Consider the bivariate joint PDF of X and Y given by (c is some constant) fxy (u, v) = otherwise 1. Find the value of c. 2. Find p(X Sys 3. Find fy(v) the marginal distribution of Y. 4. Compute p(Y |Y = ) 9. Determine whether X and Y are independent.For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 22 students, and the distribution of total study hours per week is bell-shaped with a mean of 14 hours and a standard deviation of 3.2 hours. Use the Empirical Rule to answer the following questions. a) 68% of the students spend between hours and hours on Statistics each week. b) 95% of the students spend between hours and hours on Statistics each week. c) 99.7% of the students spend between hours and hours on Statistics each week.For the following molecule, indicate the number of valence electron, the electron geometry, the molecular geometry, and the polarity. Number of valence electrons: Electron geometry: Molecular geometry: Polarity: For geometries, use the table in Appendix F. This PhET simulation may be useful. For polarity, type "polar" or "nonpolar" in the box, as appropriate.Problem 8 [MATLAB exercise] The MA'I'LAB function 'randn' is designed to generate samples of a random variable, say X , which is governed by a unit-Gaussian p.d.f. (i.e., a Gaussian p.d.f. with px = 0 and a} = 1). In this exercise, we will investigate the ability of the routine to generate truly Gaussian samples. (a) Let X be a unit-Gaussian random variable. Using pencil and paper, compute P(0 S X S 0.5) and P(0.9 S X g 1). (b) Use the MATLAB function randn to generate 1000 samples of a unit-Gaussian random variable Let's call the vector X. (c) Use the MATLAB function 'histogram' to create a histogram of the values in X with a bin width of 0.05. ((1) Plot the histogram and comment on the approximation to a unit-Gaussian p.d.f. (9) Use the histogram data to estimate the two probabilities computed in part (a). For example, No. samples in the bin covering the range 0 S X