B(t) be a Br V the transition probability density funct (3.1) P(B(10) ≤ 100) (3.2) P(B(2) ≤ 4) or B(4) ≥ 8) (3.3) P(|B(A)|B(A/2) < 2)

Example of (a) , (b) is (12),(24),(1),(6) Example of (c) (i) or (ii)   Thanks

6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, o0) is a function f such that f(r) 20 and (2) = = 1. (a) Determine which of the following functions are probability density functions on the (-x0, 00). fr-1 00 (b) We can also use probability density functions to find the erpected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. rf(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.

Consider the pdf g(y) = .06(y² + 1) on -2 ≤ y ≤ 3. (a) Calculate the probability that P(Y > 1). (b) Calculate E[Y]. (c) Calculate Var(Y).