In this paper, the properties of fuzzy Random Variables with new meter and some extended results of monotone convergence theorem and dominated convergence theorem for fuzzy Random Variables are discussed. The main result is given by usingDp, q -distance defined on the set of fuzzy numbers.

This paper extends the sign test to the case where data are observations of fuzzy Random Variables, and the hypotheses are imprecise rather than crisp. In this approach,  rst a new notion of fuzzy Random Variables is introduced. Then, the -level sets of the imprecise observations are transacted to extend the usual method of sign test. To do this, the concepts of fuzzy median and fuzzy sample median are de ned. We also develop a well-known large sample property of the classical sample median. In addition, the test statistic is extended for investigating fuzzy hypothesis. After that, applying an index called credibility degree, the degree that the observed fuzzy test statistics belongs to the critical region is evaluated. The result provides a fuzzy test function which leads to some degrees to accept or to reject the fuzzy null hypothesis. A numerical example is provided to clarify the discussions made in this paper.

The ratio of independent Random Variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice Random Variables.Ratios of such Random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) and the existing moments have been derived in terms of several special functions. The delta method is used to approximate moments.As a special case, we have obtained the PDF and CDF of the ratio of independent Rayleigh Random Variables.

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