llustrating and Calculating the Mean and Varianceof Discrete Random Variable Read and analyze the situation given below: Mr. Cresente Umal, a Mathermaties teacher, regulariy gives a formative assessment composed 5 multiple choice items. After the assessment, he used to check the probability distribution of the correct responses and the data is presented below: Test Item Probability, p(X) 0.03 0.05 0.12 0.30 0.28 0 22 Based on the data above, observe, analyze and answer the following questions: I Is the probability of x lies between O and 17 What is the sum of all probabilities of x? 1 is there a negative probability? is it possible to negative have probability? What is the average or mean of the probabilities of discrete random variable? What are the variance and the standard deviation of the probability distribution trom the data above?

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Q: Which graph correctly solves the equation below? -x²+1=x²-4

A: topic - quadratic equations

Q: 00 44 50 START!

A: From the figure  ∠1=∠3                                       ∵Corresponding angles∠1=88∘ ∠1+∠2=180∘…

Q: Evaluate 2 . ( 3 - 5 ) + 8 . 2 - 1

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Q: 39 %3D II

A: We know that  i4 =1 and i2 =-1 So that  (i4)9 = 19 i.e. i36 = 1 So that  i39 = i36 . i2 . i =…

Q: A doctors clinic evaluates incoming disposable cotton tipped applicators using the single sampling…

A: single sampling planeIf the decision about accepting or rejecting lot is taken by on the basic of…

Q: There are two more questions pleade

A: I have to answer for part-d and part-e, so i use the previous result .

Q: I need help with 13

A: By Mean value theorem, if a function f is differentiable on a, b, then there exist c∈a, b such that…

Q: s): olicities: Behavior at x-axis: (through, bounce, flatten) 2. Divide. 4x-10x+5x-7x+1 -x+2

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Q: Find ay Sin(x+y)=Cos X t cos y

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Q: Given the graph of the following equation, what is the solution? √x+27= x-3 18 6

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Q: 4. Find the 2"

A: Given problem is :

Q: Need help with number 4 letter B

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Q: Simplify the expression

A: Given:           1a3-b3 Simplify: 1a3-b3

Q: Evaluate   1 - ( 4 . 3 - 2 + 2 )

A: We have to evaluate: 1 - ( 4 . 3 - 2 + 2 )

Q: 7 25 24 A B

A: Given: A right triangle with C as 90o. AB = 25 BC =7 AC = 24     To determine: angle α

Q: asked for 9 and 10..

A: 9 is solved in previous solution, so I am giving solution for 10 :  Given :  60% from south  * 60%…

Q: [5 a = 1 b = [308] Calculate the following products and sums or give reasons why they are not…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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Q: III. Find the determinants of the following matrices using Laplace Expansion and Triangular matrices…

A: Given matrix is C = -2    7  0   6-2  1-1  3   2   2  3   4  0   5   3  2   5-4-2   2  0   3-1   1…

Q: I need help with 21

A: The given series is ∑n=1∞x-3nn25n. Let an=x-3nn25n, then an+1=x-3n+1n+125n+1. Apply ratio test,…

Q: Question c. Thanks

A: Given function is, fx=x-1+2for x<1ax2+bxfor x≥1 The objective is to find the values of a and b…

Q: 20 4.

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Q: 415 - 225= %3D

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.