2. Probablity (a) What is the distribution of Bernoulli random variable? (b) Describe the differences between a geometric and a binomial distribution. (c) Show the formula for the convolution of two random variables.
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- (i) In which case are Sobol coefficients not a good measure of sensitivity? If the model can be well approximated with a gPC expansion If many of the the higher order moments of the output are large If the input random variables are dependent(d) Prove the De Morgan's law (x + y) = x ỹ using truth-table.1) Generate 100 sample functions for the first 100 seconds of the Wiener Process by using Matlab. Have sample functions plotted in different colors on the same graph and interpret them.(MATLAB CODE REQUIRED ) a) Estimate the mean and variance functions by using the sample functions. Discuss by comparing the mean and variance functions of the Wiener Process. b) Obtain the Probability Density Function for the Wiener Process. c) Is the Wiener Process a rigidly stationary process? Show me. d) Is the Winer Process a white process? Show me.
- Consider the stochastic differential equation VX,(1- X) dWı %3D where (Wi) is a Brownian motion. This is the Wright-Fisher model in genetics: X, is the frequency of a gene (the fraction of a population of individuals that have that gene). |(a) Use R, Matlab, or some other language to generate random variates 21,..., 21024 according to the standard normal distribution. (b) Use the random variates in (a) to simulate an approximate realization of (Wt) for 0In which case are Sobol coefficients not a good measure of sensitivity ? a. if the model can be well approximated with a gPC expansion b. If many of the the higher order moments of the output are large c. if the input random variables are dependentDecay Problem My Solutions > A zircon sample contains 4000 atoms of the radioactive element 235U. Given that 235U has a half-life of 700 million years, how long would it take to decay to 125 atoms? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial Conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the period where the amount will be 125 atoms 7. Graph the solutionsComputer Science A, and B and C are bitstrings of the same length. A has a Poisson distribution. B has a normal distribution. C is uniformly distributed. What is the distribution of D=A⨁B⨁C?Decay Problem My Solut A zircon sample contains 4000 atoms of the radioactive element 235U. Given that 235U has a half-life of 700 million years, how long would it take to decay to 125 atoms? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial Conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the period where the amount will be 125 atoms 7. Graph the solutions9. Show that De Morgan's Law applies to Boolean algebra, by showing that for all x and y, (x ⋁ y)’ =x’ ⋀ y’ dan (x ⋀ y)’ = x’ ⋁ y’SEE MORE QUESTIONS