Show that if X ∼ Geom (p) then P(X = n + k | X > n) = P(X=k)  for n, k≥1.

Q: 2. For the following discrete variable with probability f(x) 1 3 4 f(x) 0.2 0.15 2c 0.05 0.15 (b)…

A: Given:

Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

A:

Q: (c) P(\X| > 3) (d) P(|X – 5| > 3)

A: We have given that.   X~N( μ , ?^2 )   μ=5 , ? =1   Z-score =( x - μ )/?

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

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

Q: How many ordered sequences are possible that contain four objects chosen from thirteen?

A: According to the given information in this question We need to find the value P( 13,4)

Q: If Z- tan () then Show that

A: According to question, z = tan-1yx

Q: Suppose that x is N(15,4). Find the P(X>11).

A: The random variable X follows normal distribution. The population mean is 15. The population…

Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: Set f(x) = In(9x - 8). Question 1 For k > 1, f (k) (1) =

A:

Q: COSZ 2) if Res(f,x) of the function f(2)=- a) -3/8 b) #-6 2ti c) 1/e d) 8/5 -is

A: To find Resf, π of the function fz=cos zz2 z-π3.

Q: A. If X~N(196,20), find x such that Pr(X < x) = 0.945.

A:

Q: Which of the following is a critical number of f(x)= 4. 2x %3D

A: The given functIon is: f(x)=14x2-2x

Q: P(|X|>1.3)

A: In statistics, the t-distribution is a probability distribution that arises in hypothesis testing…

Q: 6-2 x and y are independent and uniform in the interval (0, a). Find the p.d.f. of (a) x/y,

A:

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: X1 X2 X3 S2 R.H.S 1 9-0 11-20 7/30| 24-30 X1 1 6. 2/3 -1/6 6 X2 -1 -1/3 1/3 12 a) O<O9 b) O<O520/3…

A: Remark: Optimality condition for Simplex method:  The Optimality condition is reached at the…

Q: P(x) = . Let and let = 10. Find P(9) x!

A: We have to find p(9)

Q: s) Let f(x) 1 and g(x) 4 + 6. - х — 6 Then (fo g)(x) = (go f)(x) =

A:

Q: Suppose P(Xi=1)=pi=1-P(Xi=0),  i=1,2 if p1> p2 show that X1>( greater than equal to (st)) X2

A:

Q: 34) Deter mine the function at which points, xス f(x ) = if xE if XE IRI& -x2 is contiìNUOUS.

A:

Q: - (10 points) Show |a – b| < |a| + [b| Va,b eR.

A: We have to show that  a-b≤a+b      ∀a, b∈ℝ

Q: Let p denote 3x E Z such that P(x)" and q denote dx E R such that P(x)". Ğive a simple definition…

A:

Q: Let x, y E N, determine each of following statemen is true or false (N means Natural number, natural…

A:

Q: (7) If x < 0 then 1/x < 0. (8) If 0<x<y then 0 <1/y < 1/x

A:

Q: Define f: N→ N by f(n) = 2". Find range(f).

A:

Q: Find the CDF of the distance of two randomly chosen points of the [0,11] interval. F(x) = if x11.

A: Solution - Given that, Find the CDF of the distance of two randomly chosen of the [0,11] interval

Q: 5) Given f(x) = V1 -x² , the range is: a) O (-∞; -1] b) O [-1, 1] c) O All real numbers d) O [[0,…

A: The graph is shown below:

Q: 5(x+1) =x+1 if x = 1. O True O False

A: By solving this equation we get,