5. Distributions (a) Write down the formula for the density of the exponential distribution. (b) What does it mean that a random variable coming from an exponential has no memory? (c) Prove that an exponentially distributed random variable has no memory.
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- Show that F(x, y, z) = xy + xz + yz has the value 1 if and only if at least two of the variables x, y, and z havethe value 1.Computer Science Q. Take the data of corona virus for the year 2021 in the form of number of cases and death rate and compute the predicted values of y, using linear regression equation. Show all the calculation steps clearly also plot the graphs.A baseball is hit such that it travels straight upward after being struck by the bat. A fan observes that it requires 3.00 s for the ball to reach its maximum height. Find (a) its initial velocity and (b) its maximum height. Ignore the effects of air resistance.
- Each year a certain amount of money is deposited in an account which pays an annual interest rate of are so that at the end of the year the balance in the account is multiplied by a growth factor of X equals 2+ R. $500 is deposited at the start of the first year, an additional 200 is deposited at the start of the second year, and 600 and start of the following yearGiven A = {1,2,3} and B={u,v}, determine. a. A X B b. B X B(Oceanography) The pressure, P, exerted on an underwater object can be determined by this formula: P=gh is the density of water, which is 1.94slug/ft3 . g is the acceleration caused by Earth’s gravity, which is 32.2ft/sec2. h is the object’s depth in the water in feet. a. Determine the units of P by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for pressure listed in Table 1.1. b. Determine the pressure on a submarine operating at a depth of 2500 feet.
- Solve Both Problem A and B. Use the information from A to solve B5. (a) Write a function that solves the general linear least-squares problem. The inputs to your function should be a vector of a values, a vector of measured y values, and an anonymous function that calculates a single row of the Z matrix. Inside your function, use the inputted anonymous function to create Z row-by-row, then use Z to create the normal equations. Solve these normal equations to obtain the computed coefficients that define the best-fit of your model. Your function should output these calculated coefficients. Again, include an error check that makes sure the input vectors are the same size. You may not use any built-in MATLAB functions to solve the normal equation. You can use any functions you have developed solves Ax = b via LU-decomposition is one option. e.g. a function you have that (b) Test your function in (a) to fit the following model to the given dataset (see belo y = a + bx (c) Test your function in (a) to fit the following model to the given dataset…Computer Science Could you please solve it? Show the probabilities of all output numbers for epochs = 10.
- 101 (The epidemic model) Introduce a new unknown D (’dead people’) in model (1.1) (script) and derive a reasonable extension of the model. If possible, try to analyse your result in terms of nondimensionalization, steady states, existence of solutions, long-time behaviour of solutions...Incident Computation The sum of the years “at risk” of these 12 courses is 102 students-years, and there were 3 occurrence of disease. We can now compute the incident rate: (One decimal place only. No need to include “%” sign to your answer.)A person places $5000 in an account that accrues interest compounded continuously. Assuming no additional deposits or withdrawals, how much will be in the account after seven years if the interest rate is a constant 8.5 percent for the first four years and a constant 9.25 percent for the last three years?