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Yes, "14kt" indicates that the item is made of 14 karat gold, which means it contains 58.3% pure gold and 41.7% other metals. The "p" in "14ktp" likely refers to a plating process, suggesting that it may be gold-plated rather than solid gold. To ensure its authenticity, you can check for official markings or have it tested by a professional.

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4mo ago

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The range of Fx equals 5 2x is all positive real numbers?

True


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Gold-185 is a real chemical type of gold


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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

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