Yes, when you read Fx aloud can you can shorten it to F of x.
at first draw the graph of fx, then shift the graph along -ve x-axis 21 unit
Yes.
y=x
x = ¼x^4 + 4x + k where k can be any number
Negative the derivative of f(x), divided by f(x) squared. -f'(x) / f²(x)
[fx] is a function of x, it usually used in graphs.
Yes, when you read Fx aloud can you can shorten it to F of x.
3
if x is compact, you are simply multiplying the compact number, therefore, 'fx' will also be compact.
Motorweek - 1987 Infiniti FX 27-37 was released on: USA: 16 May 2008
The answer depends on what fx is!
(1,0)
g(x) = x/2
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
fx=3x-5 f=(3x-5)/x f2=(6x-10)/x /=divide
If x and f are quantities then xf and fx are the same if they belong to a commutative space. If not, they normally do not. Multiplication of matrices, for example is cont commutative. In fact, it is quite possible that xf has a value but fx does not even exist. if x and f are functions then again, fx and xf will not generally be the same. For example suppose x = "add 5 to it" and f = "square it". Then xf(3) = x(9) = 14 while fx(3) = f(8) = 64