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

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

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(2, 9). Compute P(1 ≤ X < 7).

A: From the provided information, Mean (µ) = 2 Variance (σ2) = 9 X~N (2, 9)

Q: 19. The interval for function |(3 )/2 z-1|<2 is -2/3 ,21 (- 2/3 ,2) (-2/3 ,2] - 2/3 ,2)

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Q: g(x) = 4 (1 + (1 over x) + (1 over x2)), [-5 , 5]   a.) Find the critical numbers and points of…

A: The given function is: g(x)=41+1x+1x2 ;       -5≤x≤5

Q: 2. (a) Let A = {x = [0, 1]: x has a decimal representation not containing the digit 5.} Show that A…

A: We shall use certain results from measure theory

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: 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)

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Q: 5. Find the domain off(z-In(e*-3). Then find f-1 and its domain.

A: f(x) = ln(ex-3)The function "ln" is defined for positive numbers only.Hence, x should be such that…

Q: 2.1.1. Let f(r1, x2) = 4.012, 0 < 1 < 1, 0 < x2 < 1, zero elsewhere, be the p of X1 and X2. Find…

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Q: Let Z~ N(0, 1). Find P( - 2.4 < Z < 0.9). Submit Question

A: Solution-: In this case, Z is the standard normal random variable with μ=0 and σ=1. Mathematically,…

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: 3. Determine the x interval(s) on which the function is increasing.

A: From the given Figure, it is observed that the graph of function has local maximum at x=-4  and…

Q: 18.12. Let the function f be entire and f(z) → o as z 0o. Show that f must have at least one zero.

A: We are given that f be entire and f(z) goes to infinity as z →∞  and we  have show that f has at…

Q: 4. Let f and g be functions defined on an open interval I containing the point c. Prove that if f…

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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 +…

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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: 1. Let N = {1, 2, 3,...} and let f: N→ N be a function given by f(x) = 2x + 3. (i) Find f(f(4) + 1).…

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Q: Find the intervals on which the function is continuous. 45) 4х, f(x) = 3 -3, -x2 + 1, -1 sx < 0 0…

A: Please refer the attached image for complete solution. THANK YOU.

Q: 6. Determine all functions f analytic in |2|< 1 and satisfying ƒ(²-) = k+k² 1+k2' k = 2,3,4,...

A: We have to determine all the analytic functions f  in  z&lt;1  such that  f1k = k+k21+k2 ,  k = 2,…

Q: 2. Let f be the arithmetic function defined by f(n) = (-1)". Compute Z;(2) = f(n) n2 n=1 Hint:…

A: Solution: We will use the following formula Here n0=2

Q: Let n EZ. Show that f(x)= x³ – nx +2 is irreducible over Q for n+-1,3,5. 72

A: Given: fx=x3-nx+2, n∈ℤ. To show fx is irreducible over ℚ for n≠-1,3,5.

Q: Find the value for z if P( Z < z ) = 0.7298.     -0.74     -0.61     0.74     0.61

A: Given that, P-value = 0.7298 Left tailed

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: Express the given integral f, 2x dx as the limit of Riemann sum. a. 2x dx = lim E-(1+) G+1)* E- d.…

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Q: - Expand f(x) = ;-X<XLO ~) = { ² }); ; OLXLX in F.S.

A:

Q: 21. Let f(n) = [/n] – [/n – 1]. Prove that f is multiplicative but not completely multiplicative.

A: See the attachment

Q: 4. For U, iid uniform on [-0,0] show that – min, {U} is sufficient for 0 > 0.

A: # random variable ui follow uniform distribution (-theta,0) then to show that  -min(ui)  be the…