Doubling down. recall the dice game played between alice and bob: alice rolls two dice, and tells bob the sum; then bob guesses a number from 1 to 6. bob wins the game if his guess appears on either of the two dice. now suppose alice and bob play for money. if bob wins, he wins a dollar, and if he loses, alice wins a dollar. we can model this using a random variable w representing bob’s winnings. we saw that using an optimal strategy, bob wins with probability 5/9. this means eii|-(1)(5/9)+(-1)(4/9)-1/9to make the game more interesting, alice allows bob to "double down": this means that after alice tells bob the sum, bob is allowed to double his bet from one dollar to two dollars, if he so chooses. give an optimal strategy for bob (for both his guess and the double-down decision) and compute e[w] for this strategy. hint: if z is a random variable representing the sum of the two dice, compute e[w] using the law of total expectation:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

5y

step-by-step explanation:

no ,sorry if you needed it but you can ask and try to see if any one will anwser ,

step-by-step explanation:

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have a nice day

no association

step-by-step explanation:

if you have eyes and you can use them efficiently you can see that it just looks like random dots like do a line of best fit and like they're so spread out it's such a weak association you might as well consider it nonexistent