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What best describes the function below fx equals 2x2-3x plus 1?
B- It is a many-to-one function
What is domain and range of random variable?
Let S denote the sample space underlying a random experiment with elements s 2 S. A random variable, X, is defined as a function X(s) whose domain is S and whose range is a set of real numbers, i.e., X(s) 2 R1. Example A: Consider the experiment of tossing a coin. The sample space is S = fH; Tg. The function X(s) = ½ 1 if s = H ¡1 if s = T is a random variable whose domain is S and range is f¡1; 1g. Example B: Let the set of all real numbers between 0 and 1 be the sample space, S. The function X(s) = 2s ¡ 1 is a random variable whose domain is S and range is set of all real numbers between ¡1 and 1. A discrete random variable is one whose range is a countable set. The random variable defined in example A is a discrete randowm variable. A continuous random variable is one whose range is not a countable set. The random variable defined in Example B is a continiuos random varible. A mixed random variable contains aspects of both these types. For example, let the set of all real numbers between 0 and 1 be the sample space, S. The function X(s) = ½ 2s ¡ 1 if s 2 (0; 1 2 ) 1 if s 2 [ 1 2 ; 1) is a mixed random variable with domain S and range set that includes set of all real numbers between ¡1 and 0 and the number 1. Cummulative Distribution Function Given a random variable X, let us consider the event fX · xg where x is any real number. The probability of this event, i.e., Pr(X · x), is simply denoted by FX(x) : FX(x) = Pr(X(s) · x); x 2 R1: The function FX(x) is called the probability or cumulative distribution fuction (CDF). Note that this CDF is a function of both the outcomes of the random experiment as embodied in X(s) and the particular scalar variable x. The properties of CDF are as follows: ² Since FX(x) is a probability, its range is limited to the interval: 0 · FX(x) · 1. ² FX(x) is a non-decreasing function in x, i.e., x1 < x2 Ã! FX(x1) · FX(x2): 1 ² FX(¡1) = 0 and FX(1) = 1. ² For continuous random variables, the CDF fX(x) is a unifromly continuous function in x, i.e., lim x!xo FX(x) = FX(xo): ² For discrete random variables, the CDF is in general of the form: FX(x) = X xi2X(s) piu(x ¡ xi); x 2 R1; where the sequence pi is called the probability mass function and u(x) is the unit step function. Probability Distribution Function The derivative of the CDF FX(x), denoted as fX(x), is called the probability density function (PDF) of the random variable X, i.e. fX(x) = dF(x) dx ; x 2 R1: or, equivalently the CDF can be related to the PDF via: FX(x) = Z x ¡1 fX(u)du; x 2 R1: Note that area under the PDF curve is unity, i.e., Z 1 ¡1 fX(u)du = FX(1) ¡ FX(¡1) = 1 ¡ 0 = 1 In general the probability of a random variable X(s) taking values in the range x 2 [a; b] is given by: Pr(x 2 [a; b]) = Z b a fX(x)dx = FX(b) ¡ FX(a): For discrete random variables the PDF takes the general form: fX(x) = X xi2X(s) pi±(x ¡ xi): Specifically for continuous random variables: Pr(x = xo) = FX(x+ o ) ¡ FX(x¡o ) = 0: 2
How do you write 6x-y equals 1?
5
What is 4x squared plus 5x plus 1 - 4x squared -6x simplified?
4x2 + 5x + 1 - 4x2 - 6x = - x + 1 or 1 - x4x2 + 5x + 1 - 4x2 - 6x = - x + 1 or 1 - x4x2 + 5x + 1 - 4x2 - 6x = - x + 1 or 1 - x4x2 + 5x + 1 - 4x2 - 6x = - x + 1 or 1 - x
Find the average value of the function on the given interval fx equals 2x to the power of3 open parentheses 1 plus x squared closed to the fourth power?
You need to clarify the function AND provide an interval.
Write 6x- 5 in function form?
1
What is the quadratic function of x2 plus 6x-7?
x2+6x-7 = (x+7)(x-1) when factored
How do you find the derivative of y equals 7e-6x?
13
Explain how the graph of fx ln x be used to graph the function gx ex -1?
graph gx is the reflection of graph fx and then transformed 1 unit down
What best describes the function below fx equals 2x2-3x plus 1?
B- It is a many-to-one function
What is the inverse function of f fx equals sqrt2x-1?
3
What are the zeros of the function f(x) 16x2 - 6x - 1?
You can use the quadratic formula for this.
What is domain and range of random variable?
Let S denote the sample space underlying a random experiment with elements s 2 S. A random variable, X, is defined as a function X(s) whose domain is S and whose range is a set of real numbers, i.e., X(s) 2 R1. Example A: Consider the experiment of tossing a coin. The sample space is S = fH; Tg. The function X(s) = ½ 1 if s = H ¡1 if s = T is a random variable whose domain is S and range is f¡1; 1g. Example B: Let the set of all real numbers between 0 and 1 be the sample space, S. The function X(s) = 2s ¡ 1 is a random variable whose domain is S and range is set of all real numbers between ¡1 and 1. A discrete random variable is one whose range is a countable set. The random variable defined in example A is a discrete randowm variable. A continuous random variable is one whose range is not a countable set. The random variable defined in Example B is a continiuos random varible. A mixed random variable contains aspects of both these types. For example, let the set of all real numbers between 0 and 1 be the sample space, S. The function X(s) = ½ 2s ¡ 1 if s 2 (0; 1 2 ) 1 if s 2 [ 1 2 ; 1) is a mixed random variable with domain S and range set that includes set of all real numbers between ¡1 and 0 and the number 1. Cummulative Distribution Function Given a random variable X, let us consider the event fX · xg where x is any real number. The probability of this event, i.e., Pr(X · x), is simply denoted by FX(x) : FX(x) = Pr(X(s) · x); x 2 R1: The function FX(x) is called the probability or cumulative distribution fuction (CDF). Note that this CDF is a function of both the outcomes of the random experiment as embodied in X(s) and the particular scalar variable x. The properties of CDF are as follows: ² Since FX(x) is a probability, its range is limited to the interval: 0 · FX(x) · 1. ² FX(x) is a non-decreasing function in x, i.e., x1 < x2 Ã! FX(x1) · FX(x2): 1 ² FX(¡1) = 0 and FX(1) = 1. ² For continuous random variables, the CDF fX(x) is a unifromly continuous function in x, i.e., lim x!xo FX(x) = FX(xo): ² For discrete random variables, the CDF is in general of the form: FX(x) = X xi2X(s) piu(x ¡ xi); x 2 R1; where the sequence pi is called the probability mass function and u(x) is the unit step function. Probability Distribution Function The derivative of the CDF FX(x), denoted as fX(x), is called the probability density function (PDF) of the random variable X, i.e. fX(x) = dF(x) dx ; x 2 R1: or, equivalently the CDF can be related to the PDF via: FX(x) = Z x ¡1 fX(u)du; x 2 R1: Note that area under the PDF curve is unity, i.e., Z 1 ¡1 fX(u)du = FX(1) ¡ FX(¡1) = 1 ¡ 0 = 1 In general the probability of a random variable X(s) taking values in the range x 2 [a; b] is given by: Pr(x 2 [a; b]) = Z b a fX(x)dx = FX(b) ¡ FX(a): For discrete random variables the PDF takes the general form: fX(x) = X xi2X(s) pi±(x ¡ xi): Specifically for continuous random variables: Pr(x = xo) = FX(x+ o ) ¡ FX(x¡o ) = 0: 2
1+6x+6x+8 =?
1+6x+6x+8 1+ 12x +8 12x + 9 = 21 + x
What does x equal in 6x-1 equals 1169?
6x-1 = 1169 6x = 1169+1 6x = 1170 x = 195
How do you write 6x-y equals 1?
5
36x squared minus 1?
When factored it is: (6x-1)(6x+1)
