Question

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 is a random variable with probability mass function : 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?

Answer 1

+ f(x) = kx + 125 x=0, 1, 2, 3, 4 find K cil flag7,0 (10) Ef(x) = 1 Hence {flol) = 1 =) (k.o+128) + (1K+125) + (2x+125). +(36+125) 7146+125) lokt 625=1 lok=1-625 ke-624 lo =-62.4 Ik – 62.4 Hence (30) - 2 3 4 2. lfca) [12562.60.2 -622-1246 CS Scanned with CamScanner

140어 130 20 1 110 100 : go- 80 - 0 So- 40 10의 20 -30 40 -- ~60 너어 B0- ) - - oi ~ 1601 110 12 1136 시니어 CS Scanned with CamScanner

let f(x) = {xfta) = 0x125 + 1x 6.2.6 + 2x0.2 + 3(-62. 2) + 4 X (-124.6) -0.t 6206 +0.4-186.6 -498.4 = 62.6 +0.4 -187.8-498.4 12 - 623 let We know that F(x) = p (x sx) Sa f(x) dx = Set 125) 4x [k 22 + 125x] 2 E-0 + [ kot 1258) D CS Scanned with CamScanner

0 2134 O 93.8/187.6 Hence F(x) = K x2 +1252 at ka-62.4 2 X 1 2 314 93.8 125.2 94.210.8 130 120 110 loo got 80- not so + 40 30 d 3 4 5 CS Scanned with CamScanner