6. Suppose there are two light bulbs in a box, one of which has lifetime (in hours) distributed as a uniform on (0, 10) and the other of which has lifetime (in hours) distributed as an exponential with rate 1/6. You pick a bulb at random, plug it in, and it is still working after 6 hours. Given this, what is the probability it will last (at least) 6 more hours?

Q: What is the coefficient of x²wa³b in the expansion of (x+y+w+a+b)??

A: To determine the coefficient of x2wa3b in the expansion of x+y+w+a+b7.

Q: Using the Binomial Theorem & Pascal's Triar expand the binomial, (a - b)* A. a -4ab3 + 6a?b? - 4a³b…

A:

Q: How many terms are there in the multinomial expansion of (x₁ + x₂ + ...........+xr)n?

A: Multinomial expansion :  (X1 + X2 + X3 + ......Xr)n  We have to calculate no. of terms in this…

Q: 4 Evaluate -1 0 5 by: 3 - 2 expanding along the first row expanding along the second column A A 1.…

A:

Q: 7 and N{B} 3 and N(A U B) = 10, how are If N{A} A and B related?

A: Given: NA=7, NB=3, NA∪B=10 We know that if NA+NB=NA∪B then there is no common element exist in Aand…

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

A:

Q: 12 Find the term of (a – 3b)" that has b in it.

A:

Q: Select and order the steps to prove the special product pattern for the square of a binomial. Step…

A: A square of a binomial is of the form (c+d)2  We first write it as a product (c+d)(c+d)Then we…

Q: Find the term indicated in the expansion (x + 2y)6; third term.

A: Find the term indicated in the expansion (x + 2y)6; third term.

Q: Use the binomial theorem (more than once) to expand (a+b+c)³.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Factor 10k + 1 into a product of primes for k = 1, 2, 3, 4, 5.

A: The main objective is to factor p(k)=10k+1 into product of primes for k=1,2,3,4,5.

Q: In the expansion of (x + y)14 which term has the highest coefficient ? O a. x10y4 O b.x7y7 Oc x14 d.…

A:

Q: 2. Use the Binomial Theorem to expand (3x - 2)6

A:

Q: How many terms are there in the expansion of (4.x + 7y)0.+ (4x- 7y)10 ?

A:

Q: 7. How many terms are there in the multinomial expansion of (x₁ + x₂ + ... .+x)"? ******..

A: We want to find the number of terms in the multinomial expansion of x1 + x2 + ... + xrn

Q: 42. The term that does not contain x in the expansion of 8x +

A:

Q: 10. 15gr, 20s

A: Given

Q: What is the 5th term in the expansion of (2x²y³ – ¹y)° O 14.25x7 y 20 15.75x10 y 19 15.05x¹0y17…

A: Given: 2x2y3-14y9=2x2y3-y49

Q: (3) Find the prime factorization b. 180

A:

Q: | (16 – 2*) dz =

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

Q: 4. Find the 11th term in the expansion of 25 3x + 5xi

A:

Q: 2/5 +7/12

A: Please see the answer below.

Q: 8) Expand the following binomial expression: (x² - 3)4.

A: o expand the binomial expression (x² - 3)^4, we can use the binomial theorem which states that: (a +…

Q: 3 3/4 + 2 7/28

A:

Q: 4) /

A: Using By Parts rule of integration.

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

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.