16. Consider a renewal process N(t) with associated distribution function F(x). Define m(t) = E[N(t)]. Show that m(t) satisfies the renewal equation ma(1) = z₂(1) + √m(t—t) dF(t), where (1) JE()‚‹- Hint: Use the renewal argument. k= 1, 2, ..., m(t-t) dF(t).

Q: How many even 3-digit numbers can be formed from the digits 1, 3, 4, 8, and 9 with no repetitions…

A: Out of the total 5 digits 1, 3, 4, 8 and 9 given, the even digits are 4 and 8. For the 3- digit…

Q: 2/18 – 12/32 + 3V50

A: The solution is given below in the next step:

Q: How many ordered triples of letters are there taken from the letters A, T, C, and G?

A: given letters: A,T,C and Gtotal number of letters = 4

Q: 1/3+2/9

A: Given 1/3 + 2/9

Q: Find L{1}ℒ{1}.

A:

Q: Prove that X Pn dx %3D

A: Recurrence relation.  Partial fraction.

Q: 10 8/10 + 9 7/12=

A:

Q: 4. Determine (16-912) dt c4

A: We will solve the problem.

Q: Simplify.2 Express 0(3n° – 2n² + n) n) as:

A: Given that O(3n^3 - 2n^2 + n)

Q: -7 5 1 9 0 -2 -1 2 -1 4

A:

Q: 4n – 1

A:

Q: 3 1/4 + 7 1/8

A:

Q: 7/2 + 3 4/6

A:

Q: 4 3/4 - 2 5/6

A: Given that the expression is

Q: 1 7. 27 2.

A:

Q: Prove that the number of partitions of n into at most k parts is equal to that of partitions of n +…

A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

Q: find  3/4 + 1/8

A:

Q: 2

A: The Laplace inverse can be found by splitting the expression into three parts as it have power of 3…

Q: 16 2/5- 8 4/9

A:

Q: 20/5+5+2*8

A: Consider the given expression

Q: Randomly drawing and immediately three red M&Ms in a row from a bag that contains 10 red M&Ms out of…

A: Given: 30 total M&Ms in that 10 red M&Ms.

Q: ne binomial:

A:

Q: Expand (a −b)4

A:

Q: -3 -10

A: The given equation is:  -3   2÷-10    7

Q: 9 5/12 - 3 2/3 =

A: Case 1: Let the given number be in mixed fraction notation.

Q: 10. 15gr, 20s

A: Given

Q: expansion of (1-2m)“

A:

Q: | (16 – 2*) dz =

A: To find : the value of ∫0216-x4dx   Using the formula ∫abxndx=1n+1bn+1-an+1

Q: 29 Using the combination formula expand (5+x)

A:

Q: 8-12 (²

A: -83

Q: Find A.

A: Given

Q: Social networker 177 316 493 Not a social networker 83 310 393 Total 260 626 886 Let S the event the…

A: Given S = the event the Internet-using teen is a social networked, N = the event the Internet-using…

Q: 1. Use expansion along the 3rd row -4 3 1 2 -1 1 7 5

A:

Q: mplify. (76)2

A:

Q: How many different ways could you choose any 4 gumballs from the 25 gumballs in the…

A: We can choose 4 gumballs from the 25 gumballs in 25C4 ways.

Q: 1/20+1/10+1/4

A:

Q: Expand 2(c+ 3).

A: Distributive property states that if x,y and z are three real numbers then x(y+z)=xy+xz.