5. Let Z ~ N(0, 1). Find z such that P(-z < Z < z) = 0.85

Q: Suppose X ~ t5, calculate P[–1.476 ≤ X ≤ 3.365]

A: Given that random variable X follows t distribution with degrees of freedom 5

Q: Find P (-1.5 < or equal to Z < 0.2) where Z ~ N (0,1)

A: We will use Standard Normal table to find the required probability.

Q: 12. For each n € N, define A, = [0, 1+] and B₁ = [0,1]. - =1 (a) Prove that U1A,, is an interval,…

A:

Q: Suppose X~N(196,20). Find x such that Pr(X > x) = 0.619.

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the mean…

Q: Q2. | For what values of a, b and c does the function 6, x = 0 f(x) = {2x2 + a, bx + c, 0 <x < 2 2…

A:

Q: Let z(x) ~N(0,1) Prop (x > -0.56) = Prop (x ≤ -2.17) = Prop (-1.56 ≤ x ≤ 0.72) =

A:

Q: Let X~N(10,9).

A: The mean of the distribution is 10. The standard deviation of the distribution is 9.

Q: Let n:Z→ 2 the n(Z) =: %3D {3Z,1+3Z,2+3Z} {3Z,1+3Z} {3Z}

A: Let π:Z→Z3Z To find  : πZ

Q: 5.16] Use the function f (x) = xe¯ ¯x² to find fave on [0,4] %3D

A:

Q: (a) Let the interval a, b be divided into n equal sub-intervals such that a = x0 < a1 < x2 < x3…

A: From this general formula we can obtain different integration formulae by putting n=1, 2,3 etc. We…

Q: Let F(x) = f(x) = x" for x = [a, b] and some positive odd integer n. Show [₁ 62_a²n 2 fdF =

A:

Q: Find the interval of En=o 2"(z – 3)" O (3.5, 0) O (2.5, 0) O (2.5, 3.5) O (2, 3)

A:

Q: Show that it is not true that for every error 1/m there exists n such that |Ek=1 polt – r/(1 - r)| <…

A: We will show that for every m there does not exist any unique n that works for all r in (0,1)

Q: 1 Expand f(2) = -in the domain 4 < |2 < 12 (z-4)(z–12)

A:

Q: LetZ~N(0,1). (a) Compute P (Z > 2)

A: Given that Z~N0,1 a) P(Z&gt;2)=1-P(Z≤2)               =1-0.9773, from the standard normal table…

Q: let x ~ N (10,2) Calculate P(x>10.5)

A: Given

Q: Suppose Z~N(0,1). Use Excel to find Pr(0.27 < Z < 1.29).  Enter your answer as a decimal rounded to…

A: Given,P(0.27&lt;Z&lt;1.29)

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

A:

Q: Show that f is continuous on (∞ , -∞ )  .

A: we have to show that f(X) is continuous in (-∞,∞). f(x)=x2             if   x&lt;1           x…

Q: For what value of a, m and b does the function { 3 x = 0 -x2 + 3x + a 0 < x < 1 1< x < 2 g(x) = mx +…

A:

Q: Verify the mean value theorem for the function f (x) = /25 – 2 over -5, 3 and find all the possible…

A:

Q: For the data x 0 0.3 0.6 0.9 1.2 f (x) 1 1.8221 3.3201 6.0496 11.0232 where the function f is…

A: Lagrange's polynomial is defined as: p(x)=∑i=0nLi(x)f(xi). Here, Li(x) are the cardinal functions.…

Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: a)Find the average of the function f(x)= x² +1 on the interval [-1,2] Answer:

A:

Q: If Z~N(0,1), then what is Pr(-0.09 < Z < 2.54)? You can use Excel. Enter your answer as a decimal…

A: We have to find given probability

Q: If X is uniform on [-2,2] then p(x <3) = 3/4 O O o o

A: Given  X~Uniform(-2,2) Pdf of X is  f(x)= 1/4     , -2&lt;x&lt;2       = 0         , otherwise

Q: 5.07 Suppose X ~ uniform(1.0,5.0). Obtain P(X > 2.4 | X < 4).

A: X~U(1,5) P(X&gt;2.4/X&lt;=4)= ?

Q: Show that x+1/x is increasing on [1,∞]

A:

Q: Let f(x,e) = ex®-1 0<x<1 then the sufficient statistics for 0 is Select one: a. - e O b. In(0) C.…

A: The joint distribution X1 , X2 , ..., Xn  is given by  fx1,x2,...,xn ; θ = ∏i=1nf(xi;θ) ,…