Nick and penny are independently performing independent bernoulli trials. for concreteness, assume that nick is ipping a nickel with probability p1 of heads and penny is ipping a penny with probability p2 of heads. let x1; x2; : : : be nick's results and y1; y2; : : : be penny's results, with xi bern(p1) and yj bern(p2). (a) find the distribution and expected value of the rst time at which they are simultaneously successful, i. e., the smallest n such that xn = yn = 1. hint: de ne a new sequence of bernoulli trials and use the story of the geometric. (b) find the expected time until at least one has a success (including the success). hint: de ne a new sequence of bernoulli trials and use the story of the geometric

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

answer: 0.26

i used the calculator on google

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

answer:

idk

step-by-step explanation: