Suppose the pdf of X is given by = {1+² 0 f(x) = (1/3+²³ × 0≤x≤2 otherwise ✪ Derive F(x). Calculate P(1 ≤ X ≤ 1.5) and P(X > 1).

Q: Find the value of the constant c that makes the following function co f(x) = = uous [cx + 7 cx² 7 if…

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Q: f X~N(196,20), find x such that Pr(X < x) = 0.563.

A: Given data  X~N(196,220) Normal distribution with mean=196 and standard deviation =20 P(x&lt;X) =…

Q: For f(x) = 2-x4/3 + x, use the 2nd- Deriv. Test to find any local max or min

A: to find local max or min.

Q: Suppose that ƒ′(x)&lt;= 1 for 1&lt;= x&lt;= 4. Show that ƒ(4) - ƒ(1)&lt;=3.

A: Show that:

Q: Let f be a differentiable function such that 2 < f'(x) < 4 for all values of x. Show that 10 < f(12)…

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Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Consider the function f(t) defined as f(t)= 2t^(2) + 8t+9 for the range -<ts, and extended…

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Q: 3. Suppose f(x) = x ^ 4 - 4x ^ 2 + 6, and g(x) = 3x ^ 3 - 8x. Prove, via the %3D %3D Intermediate…

A: By rule we solve only first question i.e. Q3 3) Given f(x)=x4-4x2+6g(x)=3x3-8xTo prove the functions…

Q: If 7х- 5,х <1 { h(x) = 3x2 – x , 1 < x< 3 Is h(x) continuous at (x=1)?

A: Continuity of function at a Point : Suppose a function f:A→B where A,B⊆ℝ .Then f is continuous at…

Q: Show that the equation 5 = x has at least one real root. You %3D may assume that the functions 5 and…

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Q: If f(x) = x² - ²x² 5 4 5 4 has a relative maximum? 3 -x³+60, then what is the set of x values for…

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Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: Show that -1/2&lt;= x/(1 + x2)&lt;=1 /2 for every value of x.

A: We need to show that -1/2&lt;= x/(1 + x2)&lt;=1 /2 for every value of x.