Using the Gaussian Probability Density function write a function that will calculate the probability that variable x will be in the range µ − ασ < x < µ + ασ, where α is some multiple of the variance.

Please help step by step with Program R (CS) with a final code for understanding thank you

Which one/s of the following is/are NOT  correct statement/s about sigmoid function? Group of answer choices a. It is non-linear. b. It is differentiable for all inputs values. c. Its gradient increases monotonically. d. Its output ranges from 0 to 1.

There are three financial aid counselors. If a student’s last initial is from A – H, let them know that their counselor is Jon Stewart. If a student’s last initial is from I – Q, let them know that their counselor is Chelsea Handler. If a student’s last initial is from R – Z, let them know that their counselor is Brian Williams.Ask student for the FICO score, if it’s less than 660 tell that this student cannot have a loan.

X is a discrete random variable with the following PMF: P(X = 1.4) = 0.25 P(X = -9.7) = 0.25 P(X = 10) = 0.5 Find the standard deviation of X.

A box contains three fair coins, and two trick coins that have heads on both sides.(a) What is the probability that a randomly selected coin from the box will come up heads whenflipped?   (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is theprobability that it’s one of the trick coins?   (c) Let X be the random variable that represents the number of heads when every coin in the box isflipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes,or you can remember that coin flips are independent of each other.)   (d) What is the expected number of heads when all the coins are flipped?Page 2

The sample space of a random experiment is (a, b, c, d, e, f, and each outcome is equally likely. A random variable is defined as follows: outcome X с d TEISEER 1.5 1.5 a b 0 2 Determine the probability mass function of X. Use the proba- bility mass function to determine the following probabilities: (a) P(X= 1.5) (b) P(0.5 3) (d) P(0 ≤X<2) (e) P(X=0 or X = 2)

Randomly generate 15 numbers rounded to 2 decimal places using the Numpy random function “normal()” with a mean of 20 and standard deviation of 5. Use seed of 1. Create a Pandas series of these 15 randomly generated numbers. Suppose that these numbers represent hourly wages of fifteen workers. Use a Pandas functions determine the average wage rate and the corresponding sample standard deviation Use a Boolean mask and Pandas function determine how many workers make less than $15 per hour Use a Boolean mask and Pandas function generate summary descriptive statistics for those earning less than $20 an hour Suppose that 5% raise for all individuals is approved. Create a new Pandas series for the new wage rate rounded to 2 decimal places

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World Series odds Consider two teams, A and B, playing a series of games until one of the teams wins n games. Assume that the probability ofA winning a game is the same for each game and equal to p, and the probability of A losing a game is q = 1− p. (Hence, there are no ties.) Let P(i, j) be the probability of A winning the series if A needs i more games to win the series and B needs j more games to win the series. a. Set up a recurrence relation for P(i, j) that can be used by a dynamic programming algorithm. b. Find the probability of team A winning a seven-game series if the proba-bility of it winning a game is 0.4. c. Write pseudocode of the dynamic programming algorithm for solving this problem and determine its time and space efficiencies.