For each of the following vectors, find a value for æ for which the vector is a probability vector. (Note: Give your answers either as rational fractions or as fractions rounded to 4 decimal places (if the fraction has more than 4 decimal places).) (1) [0.2 0.1 0.4 æ 0.2] (2) [æ 0.3 0 x 0.3] x = (3) [x 0 2x 0.6 x] (4) [4x 3x 2x 4x 5x]

Q: Albert and Billy are playing a dice game, but not with the usual dice. Albert's die has one "6" and…

A: We have given that  Albert's die has one "6" and five "4's" while Billy's die has two "5's" and four…

Q: 2-j3 Given z = a + jb = Find a and b. 1+j

A: Given that                         z=a+jb=2-j31+j. Remember that here  j2=-1

Q: BETA FUNCTION Evaluate (a) B(3. 5). (b) B(3/2.2), (c) B(1/3. 2{3). Ans. (u) 1/105. (b) 4/15

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Q: [1 2 1 6. Let A = 201 be the adjacency matrix for a graph G with vertices v1, v2, and 110 V3. Use A?…

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Q: Find the value of c such that P(Z > c) = 0.28 %3D O a. 0.3 O b. 0.58 O c. 0.85 O d. 0.22

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Q: Determine z? for the following of ?. (Round your answers to two decimal places.) A button hyperlink…

A:

Q: For events A and B, prove that P (An B) >1– P (Aº) – P (Bº).

A: We want to prove the above result. Result: 0≤P(A)≤1

Q: 1. Let, a1 = 7 and for n 2, an An-1 express an in terms ofn. %3D ". **

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Q: If f = xi+ yj+ zk,1Fl =r,and n =, then show that grad (E) == %3D

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Q: Let ā = (1, 5) and 6 = (3,0). Find —ã – b. - - V Λ

A: Answer: <-4,-5>Explanation:For any query with the solution please ask in the comment box.

Q: Show that Ti is unbiased estimator and Tz is biared estimator.

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Q: a 3. qer 2. 3. 4. 5. 9. 24 esc % IIO dy = X Equation: 10x-1 8. 10) B. C. Directions- Create an…

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Q: х Pr Product .3 2 a .4 .4 2 7 h

A: Consider the given table, X Pr Product=X×Pr 0 .3 0 2 a .4 5 .4 2 7 b c

Q: e. S √ x e √x d x 0

A: The given integral is ∫0∞x4e-xdx To find: the given integration.

Q: Sales of milk (in liters) in company A for one week are recorded as follows. Test the hypothesis…

A: Given data, Days Sales Mon 140 Tues 170 Wed 150 Thurs 137 Fri 148 sat 175 sun 165…

Q: Let X be the outcome from rolling one die and Y be the outcome from rolling a second die. Find E…

A: Taking  X and  Y are two independent events and taking their Probability Mass Function......

Q: E (x. - x Y Show that is a consistent estimator for o is N (µ, o²).

A: ANSWER: For the given data,

Q: If we know that Pr(A U B) = 0.6 and Pr( A n B )= 0.2, can we find Pr( A) and Pr (B)?

A: We have to find wheather we can find probabiities or not.

Q: Let 13 20 x 20+ y = 2 be the equation of a curve in the xy-plane. Find the equation y = T(x) of the…

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Q: Let a be a constant. Given that ) -71 3z In(az)dz = e2 ( 28 - find In a.

A: It is given that the integration ∫1e43x2lnaxdx. Use integration by parts to simplify further. Let…

Q: Fill in the blanks. Then, choose the property of m

A: Part a,Given,           ×2=0

Q: Suppose that A and B are two positive numbers and that x = In(A) and y = In(B). Write the following…

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Q: Does it change if α is 0.05?

A: Does it change if α is 0.05?

Q: Evaluate z=x−μσn if x=92.4​, μ=17.8​, σ=1.2​, and n=63

A: Given, n=63, x=92.4​, μ=17.8​, and σ=1.2​

Q: Find zα/2 when α = .01     1.96 1.645 2.576 1.28

A:

Q: Given that Z5a = 1.53 Find the value of a. O 0.06445 O 0.01570 O 0.01260 O 0.01280

A: given that z5α=1.53            find value of α=?

Q: Gamma of 6 r(6) O a. 24 O b. 240 O c. 120 O d. 12 O e. None of the above

A: We know that Gamma(x+1) = x Gamma(x) So, the above question can be done as follows:

Q: Suppose P(Ej|E2) = 0.46, P(E2|E1) = 0.92, and P(Ej) × P(E2) =0.15. Determine P(E2), giving your…

A: Conditional probability formula : P(A | B) = P(A n B) /P(B)

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.