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4841
Probability - Gravner-64.d
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (d) Find an expression for $P(Y>10)$.
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(d) Find an expression for $P(Y>10)$.
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4842
ISI2017-MMA-19
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3-px+q=0$, then the value of the determinant $\begin{vmatrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{vmatrix}$ is $p$ $p^2$ $0$ $p^2+6q$
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3-px+q=0$, then the value of the determinant $\begin{vmatrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \g...
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4843
Probability - Gravner -18.a
A full deck of $52$ cards contains $13$ hearts. Pick $8$ cards from the deck at random (a) without replacement compute the probability that you get no hearts.
A full deck of $52$ cards contains $13$ hearts. Pick $8$ cards from the deck at random(a) without replacement compute the probability that you get no hearts.
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4845
Counting
1)In how many ways we can put n distinct balls in k identical bins? 2)In how many ways we can put n distinct balls in k identical bins such that no bin is empty?
1)In how many ways we can put n distinct balls in k identical bins?2)In how many ways we can put n distinct balls in k identical bins such that no bin is empty?
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4846
Mathematics
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4847
Random variable
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4848
Kenneth H. Rosen
Let F(x, y) be the statement “x can fool y,” where the domain consists of all people in the world. Use quantifiers to express each of these statements. (a) There is exactly one person whom everybody can fool. (b) There is someone who can fool exactly one person besides himself or herself.
Let F(x, y) be the statement “x can fool y,” where thedomain consists of all people in the world. Use quantifiersto express each of these statements.(a) There is exac...
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4851
Probability- Gravner- 75.c
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?
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4853
Invertible Matrix
Let A be a $5 × 5$ invertible matrix with row sums $1$. That is $\sum_{j=1}^{5} a_{ij} = 1$ for $1 \leq i\leq 5$. Then, what is the sum of all entries of $A^{-1}$.
Let A be a $5 × 5$ invertible matrix with row sums $1$. That is $\sum_{j=1}^{5} a_{ij} = 1$ for $1 \leq i\leq 5$. Then, what is the sum of all entries of $A^{-1}$.
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4854
Graph Theory
Please help with the following:- 1)How to determine if a graph is bipartite or not? 2)What is meant by ordered pair in case of a directed graph and unordered pair in case of an undirected graph?
Please help with the following:-1)How to determine if a graph is bipartite or not?2)What is meant by ordered pair in case of a directed graph and unordered pair in case o...
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4856
Probability - Gravner-28
A group of $20$ Scandinavians consists of $7$ Swedes, $3$ Finns, and $10$ Norwegians. A committee of five people is chosen at random from this group. What is the probability that at least one of the three nations is not represented on the committee?
A group of $20$ Scandinavians consists of $7$ Swedes, $3$ Finns, and $10$ Norwegians. A committee of five people is chosen at random from this group. What is the probabil...
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4857
Combinatorics
The number of ways six distinct balls be distributed into 3 distinct urns. If each urn contain atleast one ball are ________.
The number of ways six distinct balls be distributed into 3 distinct urns. If each urn contain atleast one ball are ________.
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4858
Probability- Gravner- 75.b
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?
What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?
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4859
ISI2017-MMA-15
The diagonal elements of a square matrix $M$ are odd integers while the off-diagonals are even integers. Then $M$ must be singular $M$ must be nonsingular there is not enough information to decide the singularity of $M$ $M$ must have a positive eigenvalue
The diagonal elements of a square matrix $M$ are odd integers while the off-diagonals are even integers. Then$M$ must be singular$M$ must be nonsingularthere is not enoug...
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4860
Probability - Gravner-51.a
Ten fair dice are rolled. What is the probability that: a) At least one $1$ appears.
Ten fair dice are rolled. What is the probability that:a) At least one $1$ appears.
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