f(x) = (kx + 1)/25 , x = 0, 1, 2, 3, 4.
1. Find the value of k that makes f a probability mass function.
Graph f.
2. What is the expected number of days a rat will spend in the
maze?
3. Find and graph the cumulative distribution of the number of days
a rat
will spend in the maze. Conditional on the fact that a rat spends
at most
3 days in the maze, what is the probability that a rat spends two
days in?
4. Suppose that a rat is to receive from this researcher a food
that costs 10
dollars for each of the first two days spent in the maze and 5
dollars for
each day after the first two days, what is the expected expenditure
of this
researcher?
Latent learning is a type of learning which is not apparent in the learner’s be- haviour at the time of learning, but which manifests later when a suitable mo- tivation and circumstances appear. In his experiments, Tolman placed hungry rats in a maze with no reward for finding their way through it. He also studied a comparison group that was rewarded with food at the end of the maze. Suppose that the number of days that a rat spends in...
Latent learning is a type of learning which is not apparent in the learner’s behaviour at the time of learning, but which manifests later when a suitable motivation and circumstances appear. In his experiments, Tolman placed hungry rats in a maze with no reward for finding their way through it. He also studied a comparison group that was rewarded with food at the end of the maze. Suppose that the number of days that a rat spends in a maze...
Latent learning is a type of learning which is not apparent in the learner’s behaviour at the time of learning, but which manifests later when a suitable motivation and circumstances appear. In his experiments, Tolman placed hungry rats in a maze with no reward for finding their way through it. He also studied a comparison group that was rewarded with food at the end of the maze. Suppose that the number of days that a rat spends in a maze...
Latent learning is a type of learning which is not apparent in the learner's be- haviour at the time of learning, but which manifests later when a suitable mo- tivation and circumstances appear. In his experiments, Tolman placed hungry rats in a maze with no reward for finding their way through it. He also studied a comparison group that was rewarded with food at the end of the maze. Suppose that the number of days that a rat spends in...
1. The density function of b is given by kx(1 - x) f(x) = { for 0 < x 51, elsewhere. (a) Find k and graph the density function. (b) Find P(1/4 < ſ < 1/2). (c) Find P(-1/2 sã < 1/4). (d) Find the CDF and graph it. (e) Find E( ), E(52), and V(5). 1. The density function of ğ is given by |kx(1 – x) o for 0 < x 51, elsewhere. f(x (a) Find k and...
1. Given f(x) = kx(9 - x2)4 0<x<3, otherwise a) Find k. f(x) 20 a pdf pro b) Calculate F(x) and the three quartiles. c) Calculate E(X2) and Var(x2). d) Calculate E(X) and Var(x). (needs more than calc 1) (Bonus)
Let f(x)= kx + 5 x-1 for x<2 for x > 2 . Find the value of k for which f(x) is continuous at x=2.
1. Consider the following function: 4x 0<x<0.5 f(x)= 4- kx 0.5 <x<1 0 Otherwise a) (5%) Determine k such that f(x) is a probability density function. b) (6%) Determine CDF of x. c) (4%) Using CDE, what is the p(x 0.75) d) (4%) Using CDE what is p(x<0.6) e) (4%) Determine E(x) Type here to search o TT
7. Given the joint density function /(x,y) =(kx (1 + 3 y*) 0<x<2,0<p?1 elsewhere a. Find k, g() h) and f(x) b. Evaluate P(-<X<1)
Graph using Rstudio: 1. Suppose four distinct, fair coins are tossed. Let the random variable X be the number of heads. Write the probability mass function f(x). Graph f(x). 2. For the probability mass function obtained, what is the cumulative distribution function F(x)? Graph F(x). 3. Find the mean (expected value) of the random variable X given in part 1 4. Find the variance of the random variable X given in part 1.