Exercise: time until consecutive successes 3 points possible (ungraded) consider a sequence, x, of independent bernoulli random variables with common success probability p 1/4. let t be the first time at which we have a success immediately following a previous success; that is, t = min{n : xn = xn-1 = success). we are interested in ein we model this problem using the following markov chain 3/4 1/4 4 f ss1 1/4 the state s denotes a success, state f denotes a failure, and state ss is an absorbing state denoting the event that we have obtained two successes in a row. calculate the numerical values of the following quantities 1. 2. 3.

-1/2 +2

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.